Mathematics of Complex and Nonlinear Phenomena



Mathematical theories underpinning different classes of phenomena possess a universal character, with the same mathematical equations appearing to govern phenomena of different nature. The Mathematics of Complex and Nonlinear Phenomena can therefore be seen as the seed for cross-fertilisation between different research areas and disciplines.

Complexity and nonlinearity are often concomitant features of real-world phenomena that are commonly associated to the notion of disorder and chaos.

Unexpectedly, disordered structures and chaotic behaviours observed from fluid dynamics, classical and quantum physics to biological systems, economic and social sciences can be related, under suitable conditions, to the emergence of beautiful ordered and stable structures, as well as coherent, cooperative or cyclic behaviours.

The formation of tsunamis and rogue waves, laser pulses, turbulence of accretion disks around black holes, phase transitions from ordered to disordered states of matter are just some examples where disorder/chaos and order/coherence arise as two sides of the same coin.

Most amazingly, mathematical theories underpinning such different classes of phenomena turn out to possess a universal character so that the same mathematical equations appear to govern phenomena of (seemingly) different nature. Hence, the Mathematics of Complex and Nonlinear Phenomena (MCNP) can be seen naturally as the seed for cross-fertilisation between different research areas and disciplines.

Northumbria's MCNP Research Group conducts interdisciplinary research aiming at impacting on challenges posed by a fast-changing world. It is engaged in ground-breaking research in the hottest areas of modern Mathematics, Physics, Biology and other sciences, including multiple international collaborations with other leading experts.

MCNP research activity focuses mainly on the advancement of mathematical methods for the extensive study of nonlinear partial differential equations and dynamical systems. This ranges from their classification to the development of analytical and numerical techniques to calculate or extract qualitative and quantitative information on their solutions, e.g. asymptotic methods, multiscale analysis, nonlinear stability analysis, bifurcation theory and methods of integrable systems.

The findings of the MCNP research group are concerned with the study of mechanisms for the formation and propagation of nonlinear classical and quantum waves, coherent and localised structures, dynamic emergence of instabilities and singularities under different regimes of dispersion and dissipation, diffraction, interference, delays, phase transitions, classical and quantum chaos, geometric structures associated to differential equations and Riemann surfaces.

Applications that are currently under investigation include the solutions of models for ferromagnetic nanostructures, topological insulators, climate components, magnetohydrodynamics, biological phenomena as cyclic rhythms in glucose regulation, liquid crystals and complex networks.

The MCNP research group has successfully received funding from EPSRC, Leverhulme Trust, London Mathematical Society.

Staff   Research fellows   Research students  
Prof Gennady El Dr Costanza Benassi Marta dell'Atti
Dr Benoit HuardDr Thibault CongyDavid Graham
Dr Ezio IacoccaGiacomo Roberti
Dr Yiping MaOleg Senkevich
Dr Antonio MoroDavid Snee
Dr Matteo Sommacal
Research projects

Dr Costanza Benassi
  • Nonlinear integrable systems and random matrix models.

  • Statistical mechanics and lattice spin systems.

  • Probabilistic representations of lattice models.

Collaborators: Dr. A. Moro, Prof. D. Ueltschi.

Dr Thibault Congy
  • Wave excitations in dispersive hydrodynamics (e.g. dispersive shock waves).

  • Integrable turbulence in the framework of the nonlinear Schrödinger equation.

Collaborators: G. El (Northumbria), M. Hoefer (University of Colorado, Boulder), M. Shearer (North Carolina State University).

Personal page:

Prof Gennady El
  • Dispersive shock waves in integrable and non-integrable systems.

  • Integrable turbulence and soliton gas with applications in fibre optics.

  • Modulational instability and rogue waves: semi-classical theory.

Collaborators: M. Hoefer (University of Colorado, Boulder), M. Shearer (North Carolina State University), M. Bertola (Concordia University and SISSA), T. Congy (Northumbria), G. Roberti (PhD student, Northumbria), S. Randoux (University of Lille), P. Suret (University of Lille), A. Tovbis (University of Central Florida).

Funding: EPSRC (2017-2010, Grant No. EP/R00515X/1); Dstl (2017-2020, Contract No DSTLX-1000116851); LMS Research in Pairs Grants (2014, 2015, 2017, 2018), the Royal Society International Exchanges Scheme (2014-2016).

Full details in the Dispersive Hydrodynamics page.

Dr Benoit Huard
  • Periodic solutions in functional differential equations with application to glucose regulation.
    Collaborators: Maia Angelova (Deakin), Ruben Fossion (UNAM), Jiaxu Li (Louisville).
    Funding: This research is funded by a Newton Advanced fellowship from the British Academy of Sciences.

  • Integrability and Riemann wave interactions in multidimensional quasilinear systems of the first order.
    Collaborators: Michel Grundland (Montreal), E.V. Ferapontov (Loughborough), Vladimir Novikov (Loughborough).
Further details: Personal page.

Dr Ezio Iacocca
  • Spin hydrodynamics: mathematical connections between magnetisation dynamics and dispersive hydrodynamics as well as physical manifestations such as long-distance spin transport, vortex shedding, and the band structure of perturbations.

  • Rapid magnetisation dynamics: model, describe, and predict the spatial and temporal recovery of magnetism from a far-from-equilibrium state.

  • Waves in artificial spin ice: studying the dispersion of linear spin waves on artificial spin ice by a semi-analytical Hamiltonian model and numerical simulations

Dr Yiping Ma
  • Nonlinear waves in optical and mechanical topological insulators.

  • Localized pattern formation in driven dissipative systems.

  • Mathematical models of meltwater features in cold environments.

Further details: Personal website.

Dr Antonio Moro
Nonlinear Conservation laws and applications
  • Classification of (multidimensional) nonlinear consevation laws realised via nonlinear partial differential equations (PDEs) of hydrodynamic type with viscosity, dispersion or dispersionless, universal behaviour of solutions and singularities.

  • Complete integrability and equations of state of mean field statistical mechanical models and random networks.

  • Integrability, Toda Lattice, KP and complexity in random matrix models.
Funding: Leverhulme Trust Research Project Grant (2018-2021, PI: A. Moro; Grant Ref. RPG-2017-228) - Dressing methods and complexity reduction for integrable networks models; Royal Society International Exchanges (2017-2019) - PI: A. Moro; Co-I: G. Biondini - p-Stars and KP: soliton phase diagrams for complex systems.

For more details click here.

Dr Matteo Sommacal
  • Nonlinear waves in ferromagnetic systems
    Short description: Localised, propagating magnetic structures in 1- and 2-dimensional ferromagnetic systems at the nanometre length-scale. Classical, continuous Heisenberg ferromagnet equation. Landau-Lifshitz equation with uni-axial and bi-axial anisotropy.

    Collaborators: Francesco Demontis and Cornelis van der Mee (University of Cagliari, Italy); Mark Hoefer (University of Colorado at Boulder, CO USA); Sara Lombardo (Loughborough University, UK); Giovanni Ortenzi (UniversitÓ di Milano Bicocca, Italy); Thomas Silva (National Institute of Standards and Technology, Boulder, CO USA).

  • Integrability and linear stability of nonlinear waves
    Short description: Linear stability analysis of scalar and multi-component, nonlinear partial differential equations of integrable type. Manakov system. Vector nonlinear Schroedinger equation. Three waves resonant interaction equation.
    Collaborators: Antonio Degasperis (University of Rome "La Sapienza", Italy); Sara Lombardo (Loughborough University, UK).

  • Complex dynamics and Riemann surfaces
    Short description: Understanding complex dynamics by means of an associated Riemann surface. Circular flow on a compact Riemann surface. Landen transformations. Slow chaos and parabolic dynamical systems.
    Collaborators: Francesco Calogero and Paolo Maria Santini (University of Rome "La Sapienza", Italy); David Gomez-Ullate (Universidad Complutense de Madrid, Spain).
Funding: LMS, Research in Pairs - Scheme 4, "Instabilities of nonlinear waves by means of elementary algebraic-geometry", Grant Ref. 41808 (2019). LMS, Research in Pairs - Scheme 4, "Propagating, localised waves in ferromagnetic nanowires", Grant Ref. 41622 (2017).

Research students

Research seminars

The group runs the weekly Mathematics and Mathematical Physics series of research seminars and colloquia. The seminars usually take place on Wednesdays at 3pm, in the MAGIC room (ELD201).

Autumn 2019

Date: 20 November 2019, 4pm.
Speaker: Prof. Roy Chantrell (University of York)
Title: All optical magnetization switching: basic physics and potential for new recording technology
Abstract: The response of a magnetic material to an ultrafast (femtosecond) laser pulse is, arguably, at the leading edge of condensed matter physics. Early experiments showed, surprisingly, that materials can be demagnetized on a sub-picosecond timescale. Later, it was discovered that the magnetization direction can be switched by circularly polarized laser light on a timescale of picoseconds. This has led to investigations of the prospects of optically switched media for ultrafast high density magnetic information storage. I will describe an atomistic model approach to the understanding of ultrafast magnetization dynamics. Among the predictions of the model is the phenomenon of thermally induced magnetization switching (TIMS) in which switching occurs in the absence of an external applied field. This is an astonishing result which was confirmed experimentally and is still not fully understood. I will begin with an introduction to some advanced applications of magnetism, including spin based electronics and advanced permanent magnets for automotive applications. These examples demonstrate the need for advanced atomistic / multiscale approaches. I will then outline the atomistic model approach and proceed to describe the experiments and model calculations leading to TIMS and its potential for application in ultra-high density recording.

Date: 13 November 2019, 3pm.
Speaker: Dr. Daniel Ratliff (Loughborough University)
Title: Entirely Out of Character? Dispersive Dynamics in the Moving Frame
Abstract: In the evolution of nonlinear waves, localised structures and defects can form and persist, and even stable waves can bifurcate to accommodate these. One way in which their formation can be understood in through the use of the Whitham Modulation equations (WMEs), a dispersionless set of quasilinear PDEs. However, a persistent problem is how to regularise this system via the inclusion of dispersive effects to prevent the emergence of multivalued wave quantities. Surprisingly, it transpires that such features already lurk within the WMEs whenever they are hyperbolic -- one merely has to wait long enough in a suitable moving frame. This takes the form of the Korteweg - de Vries (KdV) equation, which is universal in the sense that its coefficients are tied to abstract properties of the original Lagrangian. This leads to a more general question -- can the properties of the characteristics be used to infer the resulting dynamics? This is demonstrated to be true, and the connection between established concepts in hyperbolic systems (such as the Hamiltonian-Hopf bifurcation and linear degeneracy) and some well-known nonlinear dispersive equations, such as the Two-Way Boussinesq and modified KdV equations, are made.

Date: 11 November 2019, 4pm.
Speaker: Prof. Anatoly Neishtadt (Loughborough University)
Title: On destruction of adiabatic invariance
Abstract: In many problems of classical mechanics and theoretical physics dynamics can be described as a slow evolution of periodic or quasi-periodic processes. Adiabatic invariants are approximate first integrals for such a dynamics. Existence of adiabatic invariants makes dynamics close to regular. Destruction of adiabatic invariance leads to chaotic dynamics. In the talk it is planned to present a review of some mechanisms of destruction of adiabatic invariance with examples from charged particle dynamics.

Date: 6 November 2019, 3pm.
Speaker: Dr. Patrick Antolin (Northumbria University)
Title: On thermal instability and non-equilibrium in the solar atmosphere: coronal rain and long-period intensity pulsations
Abstract: The solar atmosphere is mainly composed by a dense and cold chromosphere and a tenuous and hot, extended corona. It is permeated by magnetic fields that can either be closed - forming loop-like structures called coronal loops, anchored to the solar surface - or open - allowing the gas to flow outward as the solar wind. Coronal loops are highly dynamic and are known to exhibit heating and cooling processes continuously in a state of thermal non-equilibrium. Their high million degree temperatures stem from the magnetic field, which is tressed by sub-surface convective motions and dissipated by yet unidentified processes. Recently, a subset of coronal loops have been found to exhibit clock-like behaviour, producing intensity pulsations lasting several days. During their cooling phase, the ionised gas can recombine and condense via a thermal instability to form coronal rain - a spectacular phenomenon in which cool and dense material condenses apparently from nowhere and flows back to the surface along the loops. In this talk I will introduce the concept of thermal non-equilibrium and thermal instability in coronal loops, its observable quantities and the outstanding open questions in the field.

Date: 16 October 2019, 3pm.
Speaker: Prof Cornelis van der Mee (Department of Mathematics and Computer Science, University of Cagliari, Italy)
Title: Reflectionless solutions for square matrix nonlinear Schroedinger equation with vanishing boundary conditions
Abstract: After a quick review of the direct and inverse scattering theory of the focusing Zakharov-Shabat system with symmetric nonvanishing boundary conditions, we derive the reflectionless solutions of the 2 × 2 matrix NLS equation with vanishing boundary conditions and four different symmetries by using the Marchenko theory. Since the Marchenko integral kernel has separated variables, the matrix triplet method - consisting of representing the Marchenko integral kernel in a suitable form - allows us to find the exact expressions of the reflectionless solutions in terms of a triplet of matrices. Moreover, since these exact expressions contain matrix exponentials and matrix inverses, computer algebra can be used to "unpack" and graph them. Finally, it is remarkable that these solutions are also verified by direct substitution in the 2 × 2 NLS equation.
This is a joint work with Francesco Demontis (University of Cagliari, Italy) and Alyssa Ortiz (University of Colorado at Colorado Springs, USA).

Date: 7 October 2019, 4pm.
Speaker: Prof Alexander Tovbis ( University of Central Florida)
Title: Soliton and breather gases for the focusing nonlinear Schrödinger equation
Abstract: Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles" of complex statistical objects called soliton and breather gases. In this talk, we discuss spectral theory of a generalized breather gas by considering a special, thermodynamic type limit of multi-phase (finite-gap) solutions of the focusing nonlinear Schrödinger (fNLS) equation. The family of generalized breather gases includes gas of fundamental solitons and gas of conventional breathers (solitons on finite background) as particular cases. We consider several particular cases of the generalized breather gas including the so-called bound state soliton gas, as well as some transitional regimes (condensate and ideal gas limits

Date: 2 October 2019, 3pm.
Speaker: Dr. Ezio Iacocca (Northumbria University)
Title: Rapid dynamics in solid-state magnetism
Abstract: Magnetism in solids is a fascinating yet complex phenomenon that encompasses vastly different length and time scales. This complexity is typically resolved by establishing equations that are valid at different scales. For example, magnetic dynamics at the atomic level can be described by a discrete system of Schrödinger equations while microscopic magnetisation dynamics is described by a vectorial partial differential equation known as the Landau-Lifshitz equation. However, such a distinction of scales is challenged when considering the problem of a magnetic material that dynamically evolves towards equilibrium from a randomised state. In this talk, I will give an overview of solid-state magnetism at these extreme conditions, the experimental capabilities available, and the current theoretical understanding of the underlying physical phenomena. I will also discuss the advantages of a dispersive hydrodynamic interpretation of magnetisation dynamics in the context of rapid magnetic soliton nucleation and evolution. Finally, I will outline future research directions and outstanding challenges of the research field towards technological applications.


Spring 2019

Date: 8 July 2019, 3pm.
Speaker: Michael Overton (Courant Institute, New York University)
Title: Stability optimization for polynomials and matrices
Abstract: Suppose that the coeffcients of a monic polynomial or entries of a square matrix depend affinely on parameters, and consider the problem of minimizing the root radius (maximum of the moduli of the roots) or root abscissa (maximum of their real parts) in the polynomial case and the spectral radius or spectral abscissa in the matrix case. These functions are not convex and they are typically not locally Lipschitz near minimizers. We first address polynomials, for which some remarkable analytical results are available in one special case, and then consider the more general case of matrices, focusing on the static output feedback problem arising in control of linear dynamical systems. We also briefly discuss some spectral radius optimization problems arising in the analysis of the transient behavior of a Markov chain and the design of smooth surfaces using subdivision algorithms. Finally, time permitting, we discuss optimization of pseudospectra of matrices.

Date: 15 May 2019, 3pm.
Speaker: Anna Concas (University of Cagliari)
Title: A spectral method for ''bipartizing'' a network and detecting a large anti-community
Abstract: Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover the structural properties of a network. A network is said to be bipartite if its nodes can be subdivided into two nonempty sets such that there are no edges between nodes in the same set. It is a difficult task to determine the closest bipartite network to a given network. In this talk, I will describe how a given network can be approximated by a bipartite one by solving a sequence of fairly simple optimization problems. The proposed algorithm also produces a node permutation which makes the possible bipartite nature of the initial adjacency matrix evident and identifies the two sets of nodes. It will be also showed how the same procedure can be used to detect the presence of a large anti-community in a network and to identify it.

Date: 8 May 2019, 3pm.
Speaker: Vincenzo Vitagliano (Keio University)
Title: Topological defects, deformed lattices and spontaneous symmetry breaking
Abstract: External conditions have a dramatic impact on the way symmetry breaking occurs. I will review some recent (and some less recent) results of symmetry breaking in curved spacetime. Flirting with the contemporary interest toward 2D engineered material, I will then move on potential applications on geometrically deformed lattices. In a curved background, the natural expectation is that curvature works towards the restoration of internal symmetries. I will show instead that, for topological defects, the competing action of the locally induced curvature and boundary conditions generated by the non-trivial topology allows configurations where symmetries can be spontaneously broken close to the core.

Date: 1 May 2019, 3pm.
Speaker: Daniel Ueltschi (Warwick University)
Title: From condensed matter physics to probability theory
Abstract: The primary goal of condensed matter physics is to understand the behaviour of electrons in solids. The basic laws are well understood, but the large number of interacting particles makes it challenging. A popular approach is to introduce simple models and to use the setting of statistical mechanics. I will review quantum spin systems and their stochastic representations in terms of random permutations and random loops. I will also describe the *universal* behaviour that is common to loop models in dimensions 3 and more.

Date: 20 March 2019, 3pm.
Speaker: Ian Strachan (Glasgow University)
Title: Miura transformations from Novikov algebras
Abstract: For the KdV equation, the Miura map transforms the second Hamiltonian structure into the first Hamiltonian structure. Multicomponent generalization of KdV's bi-Hamiltonian structure have been known for decades - they date back to the work of Gelfand and Dorfman, and Balinskii and Novikov - and are defined in terms of algebraic structures known as Novikov algebras. The corresponding Muira map for these structures was constructed by Balinskii and Novikov only in the case where the algebra is commutative. In this talk a construction will be presented which solves the problem of the constructive of these maps in general.

Date: 13 March 2019, 3pm.
Speaker: Gandalf Lechner (Cardiff University)
Title: Quantum-mechanical backflow and scattering theory
Abstract: Backflow is the phenomenon that the probability current of a quantum particle on the line can flow in the direction opposite to its momentum. This talk will revisit this effect in the context of potential scattering in quantum mechanics. It turns out backflow is universal in the sense that it occurs in every potential (in a large class), and has always bounded spatial extent. On a mathematical level, these results are proven by establishing (lower) bounds on the spectra of certain integral operators. These general investigations are complemented with concrete examples and numerics.

Date: 6 March 2019, 4pm.
Speaker: Riccardo Montalto (University of Milano)
Title: KAM theory for pure gravity water waves in finite depth
Abstract: In this talk I will present some recent results concerning the existence and the stability of quasi-periodic solutions for the WAVES EQUATIONS ( 2D-Euler equation of an irrotational and incompressible fluid in an ocean with finite depth under the action of the gravity). After an overview of the classical methods used in the KAM theory for semilinear partial differential equations, I will focus on the method used to deal with fully nonlinear PDEs and in particular I will describe the KAM results obtained for the water waves equation. The main difficulties are:
1) the fully nonlinear nature of the gravity water waves equations (the highest order x-derivative appears in the nonlinear term but not in the linearization at the origin)
2) the linear frequencies grow only in a sublinear way at infinity.
In order to overcome the small divisors problem, the proof is obtained by a Nash Moser iteration. The key point is to solve the linearized PDE at any approximate solution. This requires to combine perturbation theory and Pseudo differential calculus.

Date: 13 February 2019, 3pm.
Speaker: Sirio Orozco Fuentes (Newcastle University)
Title: Patterning, segregation and differentiation in human embryonic stem cell colonies
Abstract: The maintenance of the pluripotent state in human embryonic stem cells (hESCs) is highly crucial for their application in the laboratory as a tool for drug testing and the study of cell based therapies. Currently the selection of the best quality cells and colonies for propagation is done empirically in terms of their displayed features, such as a round nucleus, scant cytoplasm, prominent/abundant nucleoli and less intercellular spacing between the individuals in the bulk. Using image analysis and computational tools, we quantify these properties using phase contrast images of hESCs colonies of different sizes (0.1 - 1.1 mm2) during day 2, 3 and 4 of plating.

We identify their main characteristics such as the number of nearest neighbours, mean cell area, among other features. We discuss the mechanisms underlying the formation of these structures in vitro and explore, through a dynamical model in which the cells are represented as Voronoi tessellations of the space, how the cells might attain different levels of pluripotency and differentiate towards the three germs layers.

Date: 6 February 2019, 3pm.
Speaker: Hilmar Gudmundsson (Northumbria)
Title: The relationship between bed and surface topography on glaciers and ice sheets
Abstract: Glacier flow is an example of a gravity driven non-linear viscous flow at low Reynolds numbers. As a glacier flows over an undulating bed, the surface topography is modified in response. Some information about bed conditions is therefore contained in the shape of the surface and the surface velocity field. I will present theoretical and numerical work on how basal conditions on glaciers affect ice flow, and how one can obtain information about basal conditions through surface-to-bed inversion. I'll give an overview over inverse methodology currently used in glaciology, and how satellite data is now routinely used to invert for bed properties of the Greenland and the Antarctic Ice Sheets.

Recent publications


Bridgewater, Adam, Huard, Benoit and Angelova, Maia (2019) Amplitude and frequency variation in nonlinear glucose dynamics with multiple delays via periodic perturbation. Journal of Nonlinear Science. ISSN 0938-8974 (In Press)

Roberti, Giacomo, El, Gennady, Randoux, Stéphane and Suret, Pierre (2019) Early stage of integrable turbulence in the one-dimensional nonlinear Schrödinger equation: a semiclassical approach to statistics. Physical Review E. ISSN 2470-0045

Maiden, Michelle D., Franco, Nevil A., Webb, Emily, El, Gennady and Hoefer, Mark (2019) Solitary wave fission of a large disturbance in a viscous fluid conduit. Journal of Fluid Mechanics. ISSN 0022-1120 (In Press)

Congy, Thibault, El, Gennady and Hoefer, Mark (2019) Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves. Journal of Fluid Mechanics, 875. pp. 1145-1174. ISSN 0022-1120

Benassi, Costanza and Ueltschi, Daniel (2019) Loop Correlations in Random Wire Models. Communications in Mathematical Physics. ISSN 0010-3616 (In Press)

Lorenzoni, Paolo and Moro, Antonio (2019) Exact analysis of phase transitions in mean-field Potts models. Physical Review E, 100 (2). 022103. ISSN 2470-0045

Snee, David and Ma, Yi-Ping (2019) Edge solitons in a nonlinear mechanical topological insulator. Extreme Mechanics Letters, 30. p. 100487. ISSN 2352-4316

Ma, Yi-Ping, Sudakov, Ivan, Strong, Courtenay and Golden, Kenneth (2019) Ising model for melt ponds on Arctic sea ice. New Journal of Physics, 21 (6). 063029. ISSN 1367-2630

Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2019) The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. I. Direct and inverse scattering theory. Ricerche di Matematica, 68 (1). pp. 145-161. ISSN 0035-5038

Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2019) The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. II. IST and closed-form soliton solutions. Ricerche di Matematica, 68 (1). pp. 163-178. ISSN 0035-5038

Goussev, Arseni (2019) Equivalence between quantum backflow and classically forbidden probability flow in a diffraction-in-time problem. Physical Review A, 99 (4). 043626. ISSN 1050-2947

Bridgewater, Adam, Stringer, Ben, Huard, Benoit and Angelova, Maia (2019) Ultradian rhythms in glucose regulation: A mathematical assessment. AIP Conference Proceedings, 2090 (050010). ISSN 1551-7616

Congy, Thibault, El, Gennady, Hoefer, Mark and Shearer, Michael (2019) Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure. Studies in Applied Mathematics, 142 (3). pp. 241-268. ISSN 0022-2526

Degasperis, Antonio, Lombardo, Sara and Sommacal, Matteo (2019) Rogue Wave Type Solutions and Spectra of Coupled Nonlinear Schrödinger Equations. Fluids, 4 (1). p. 57. ISSN 2311-5521

Kraych, Adrien, Suret, Pierre, El, Gennady and Randoux, Stéphane (2019) Nonlinear evolution of the locally induced modulational instability in fiber optics. Physical Review Letters, 122. pp. 054101. ISSN 0031-9007

Haspolat, Emrah, Huard, Benoit and Angelova, Maia (2019) Deterministic and stochastic models of Arabidopsis Thaliana flowering. Bulletin of Mathematical Biology, 81 (1). pp. 277-311. ISSN 0092-8240


Congy, Thibault, El, Gennady, Hoefer, Mark and Shearer, Michael (2018) Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure. Studies in Applied Mathematics. ISSN 0022-2526 (In Press)

Demontis, Francesco, Lombardo, Sara, Sommacal, Matteo, van der Mee, Cornelis and Vargiu, F. (2018) Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation. Communications in Nonlinear Science and Numerical Simulation, 64. pp. 35-65. ISSN 1007-5704

De Matteis, Giovanni, Giglio, Francesco and Moro, Antonio (2018) Exact equations of state for nematics. Annals of Physics, 396. pp. 386-396. ISSN 0003-4916

Randoux, Stéphane, Suret, Pierre, Chabchoub, Amin, Kibler, Bertrand and El, Gennady (2018) Nonlinear spectral analysis of Peregrine solitons observed in optics and in hydrodynamic experiments. Physical Review E, 98 (2). 022219. ISSN 2470-0045

Degasperis, Antonio, Lombardo, Sara and Sommacal, Matteo (2018) Integrability and linear stability of nonlinear waves. Journal of Nonlinear Science, 28 (4). pp. 1251-1291. ISSN 0938-8974

Goussev, Arseni, Reck, Phillipp, Moser, Florian, Moro, Antonio, Gorini, Cosimo and Richter, Klaus (2018) Overcoming dispersive spreading of quantum wave packets via periodic nonlinear kicking. Physical Review A (PRA), 98. 013620. ISSN 2469-9926

Demontis, Francesco, Ortenzi, Giovanni and Sommacal, Matteo (2018) Heisenberg ferromagnetism as an evolution of a spherical indicatrix: localized solutions and elliptic dispersionless reduction. Electronic Journal of Differential Equations, 2018 (106). pp. 1-34. ISSN 1072-6691

Maiden, Michelle D., Anderson, Dalton V., Franco, Nevil A., El, Gennady and Hoefer, Mark A. (2018) Solitonic Dispersive Hydrodynamics: Theory and Observation. Physical Review Letters, 120 (14). ISSN 0031-9007

Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2018) The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. II. IST and closed-form soliton solutions. Ricerche di Matematica. ISSN 0035-5038 (In Press)

Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2018) The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. I. Direct and inverse scattering theory. Ricerche di Matematica. ISSN 0035-5038 (In Press)

Sprenger, Patrick, Hoefer, Mark and El, Gennady (2018) Hydrodynamic optical soliton tunneling. Physical Review E, 97 (3). ISSN 2470-0045

Reck, Phillipp, Gorini, Cosimo, Goussev, Arseni, Krueckl, Viktor, Fink, Mathias and Richter, Klaus (2018) Towards a quantum time mirror for nonrelativistic wave packets. New Journal of Physics, 20. 033013. ISSN 1367-2630

El, Gennady, Nguyen, Lu Trong Nguyen and Smyth, Noel (2018) Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type. Nonlinearity, 31 (4). pp. 1392-1416. ISSN 0951-7715

El, Gennady, Hoefer, Mark A. and Shearer, Michael (2018) Stationary Expansion Shocks for a Regularized Boussinesq System. Studies in Applied Mathematics, 140 (1). pp. 27-47. ISSN 0022-2526


Suret, Pierre, El, Gennady, Onorato, Miguel and Randoux, Stéphane (2017) Rogue waves in integrable turbulence: semi-classical theory and fast measurements. In: Nonlinear Guided Wave Optics: A testbed for extreme waves. IOP Publishing, 12-1-12-32. ISBN 978-0-7503-1460-2

Gaididei, Yuri, Goussev, Arseni, Kravchuk, Volodymyr, Pylypovskyi, Oleksandr, Robbins, Jonathan, Sheka, Denis, Slastikov, Valeriy and Vasylkevych, Sergiy (2017) Magnetization in narrow ribbons: curvature effects. Journal of Physics A: Mathematical and Theoretical, 50. p. 385401. ISSN 1751-8113

Benassi, Costanza, Lees, Benjamin and Ueltschi, Daniel (2017) Correlation Inequalities for Classical and Quantum XY Models. In: Advances in Quantum Mechanics. Springer INdAM Series, 18 (18). Springer, pp. 15-31. ISBN 9783319589039

Hoefer, Mark, El, Gennady and Kamchatnov, Anatoly (2017) Oblique Spatial Dispersive Shock Waves in Nonlinear Schrödinger Flows. SIAM Journal on Applied Mathematics, 77 (4). pp. 1352-1374. ISSN 0036-1399

Benassi, Costanza, Fröhlich, Jürg and Ueltschi, Daniel (2017) Decay of Correlations in 2D Quantum Systems with Continuous Symmetry. Annales Henri Poincaré, 18 (9). pp. 2831-2847. ISSN 1424-0637

Tikan, Alexey, Billet, Cyril, El, Gennady, Tovbis, Alexander, Bertola, Marco, Sylvestre, Thibaut, Gustave, Francois, Randoux, Stephane, Genty, Goëry, Suret, Pierre and Dudley, John M. (2017) Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation. Physical Review Letters, 119 (3). 033901. ISSN 0031-9007

Goussev, Arseni (2017) Rotating Gaussian wave packets in weak external potentials. Physical Review A (PRA), 96. 013617. ISSN 1050-2947

Randoux, Stéphane, Gustave, François, Suret, Pierre and El, Gennady (2017) Optical Random Riemann Waves in Integrable Turbulence. Physical Review Letters, 118 (23). ISSN 0031-9007

Reck, Phillipp, Gorini, Cosimo, Goussev, Arseni, Krueckl, Viktor, Fink, Mathias and Richter, Klaus (2017) Dirac quantum time mirror. Physical Review B, 95 (16). p. 165421. ISSN 2469-9950

Huard, Benoit, Bridgewater, Adam and Angelova, Maia (2017) Mathematical investigation of diabetically impaired ultradian oscillations in the glucose-insulin regulation. Journal of Theoretical Biology, 418. pp. 66-76. ISSN 0022-5193

El, Gennady, Hoefer, Mark and Shearer, Michael (2017) Dispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws. SIAM Review, 59 (1). pp. 3-61. ISSN 0036-1445

Chesnokov, A. A., El, Gennady, Gavrilyuk, S. L. and Pavlov, M. V. (2017) Stability Of Shear Shallow Water Flows with Free Surface. SIAM Journal on Applied Mathematics, 77 (3). pp. 1068-1087. ISSN 0036-1399


El, Gennady and Hoefer, Mark (2016) Dispersive shock waves and modulation theory. Physica D: Nonlinear Phenomena, 333. pp. 11-65. ISSN 0167-2789

Giglio, Francesco, Landolfi, Giulio and Moro, Antonio (2016) Integrable extended van der Waals model. Physica D: Nonlinear Phenomena, 333. pp. 293-300. ISSN 0167-2789

Tovbis, Alexander and El, Gennady (2016) Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach. Physica D: Nonlinear Phenomena, 333. pp. 171-184. ISSN 0167-2789

Bertola, Marco, El, Gennady and Tovbis, Alexander (2016) Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2194). p. 20160340. ISSN 1364-5021

Onorato, Miguel, Proment, Davide, El, Gennady, Randoux, Stephane and Suret, Pierre (2016) On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type. Physics Letters A, 380 (39). pp. 3173-3177. ISSN 0375-9601

El, Gennady, Khamis, Eduardo and Tovbis, Alex (2016) Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves. Nonlinearity, 29 (9). pp. 2798-2836. ISSN 0951-7715

Randoux, Stéphane, Suret, Pierre and El, Gennady (2016) Inverse scattering transform analysis of rogue waves using local periodization procedure. Scientific Reports, 6 (1). p. 29238. ISSN 2045-2322

Goussev, Arseni, Jalabert, Rodolfo, Pastawski, Horacio and Wisniacki, Diego (2016) Loschmidt echo and time reversal in complex systems. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 374 (2069). p. 20150383. ISSN 1364-503X

El, Gennady, Hoefer, Mark and Shearer, Michael (2016) Expansion shock waves in regularized shallow-water theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2189). p. 20160141. ISSN 1364-5021

Benassi, Costanza, Lees, Benjamin and Ueltschi, Daniel (2016) Correlation Inequalities for the Quantum XY Model. Journal of Statistical Physics, 164 (5). pp. 1157-1166. ISSN 0022-4715

Goussev, Arseni, Robbins, Jonathan, Slastikov, Valeriy and Tretiakov, Oleg (2016) Dzyaloshinskii-Moriya domain walls in magnetic nanotubes. Physical Review B (PRB), 93 (5). 054418. ISSN 1098-0121


Barbier, Maximilien, Beau, Mathieu and Goussev, Arseni (2015) Comparison between two models of absorption of matter waves by a thin time-dependent barrier. Physical Review A (PRA), 92 (053630). ISSN 1050-2947

Huard, Benoit, Easton, Jonathan and Angelova, Maia (2015) Investigation of stability in a two-delay model of the ultradian oscillations in glucose-insulin regulation. Communications in Nonlinear Science and Numerical Simulation, 26 (1-3). pp. 211-222. ISSN 1007-5704

Barra, Adriano and Moro, Antonio (2015) Exact solution of the van der Waals model in the critical region. Annals of Physics, 359. pp. 290-299. ISSN 0003-4916

Arsie, Alessandro, Lorenzoni, Paolo and Moro, Antonio (2015) Integrable viscous conservation laws. Nonlinearity, 28 (6). pp. 1859-1895. ISSN 0951-7715

Dubrovin, Boris, Grava, Tamara, Klein, Christian and Moro, Antonio (2015) On critical behaviour in systems of Hamiltonian partial differential equations. Journal of Nonlinear Science, 25 (3). pp. 631-707. ISSN 0938-8974

Goussev, Arseni (2015) Manipulating quantum wave packets via time-dependent absorption. Physical Review A (PRA), 91 (4). 043638. ISSN 1050-2947


Barra, Adriano, Guerra, Francesco, Di Lorenzo, Andrea and Moro, Antonio (2014) On quantum and relativistic mechanical analogues in mean field spin models. Proceedings of the Royal Society A, 470 (2172). ISSN 1471-2946

Arsie, Alessandro, Lorenzoni, Paolo and Moro, Antonio (2014) On integrable conservation laws. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471 (201401). ISSN 1471-2946

Moro, Antonio (2014) Shock dynamics of phase diagrams. Annals of Physics, 343. pp. 49-60. ISSN 0003-4916

Goussev, Arseni, Robbins, Jonathan and Slastikov, Valeriy (2014) Domain wall motion in thin ferromagnetic nanotubes: Analytic results. Europhysics Letters, 105 (6). p. 67006. ISSN 0295-5075

Dubertrand, Remy and Goussev, Arseni (2014) Origin of the exponential decay of the Loschmidt echo in integrable systems. Physical Review E, 89. 022915. ISSN 1539-3755

Moro, Antonio and Trillo, Stefano (2014) Mechanism of wave breaking from a vacuum point in the defocusing nonlinear Schrödinger equation. Physical Review E (PRE), 89 (2). ISSN 1550-2376

de Nittis, Giuseppe, Lorenzoni, Paolo and Moro, Antonio (2014) Integrable multi-phase thermodynamic systems and Tsallis' composition rule. Journal of Physics: Conference Series, 482 (1). 012009. ISSN 1742-6588

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