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 Adam Bridgewater
Dr Arseni GoussevDr Thibault CongyMarta dell'Atti
Dr Benoit HuardDavid Graham
Dr Oleg KirillovJoris Labarbe
Dr Yiping MaGiacomo Roberti
Dr Antonio MoroMarzia Romano
Dr Matteo SommacalOleg Senkevich
David Snee
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 Arseni Goussev
  • Quantum wave packet dynamics (exactly solvable systems, diffraction in time, quantum time mirrors, Loschmidt echo, quantum chaos, rotating wave packets, quantum motion in the presence of absorption).

  • Dynamics of magnetic domains (Landau-Lifshitz-Gilbert equation in various geometries and topologies).

  • Semiclassical theory of chemical reactions (reactive scattering in phase space, transition state theory)
Funding: EPSRC (Ref. EP/K024116/1), 2013-2016.

Personal 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 (R. Fossion).

  • 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 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 (Università 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. Full details can be found at the seminars page.
Recent publications


Kirillov, Oleg (2018) Dissipation-Induced Instabilities in Magnetized Flows. Journal of Mathematical Sciences. ISSN 1072-3374 (In Press)

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)

Haspolat, Emrah, Huard, Benoit and Angelova, Maia (2018) Deterministic and stochastic models of Arabidopsis Thaliana flowering. Bulletin of Mathematical Biology. ISSN 0092-8240 (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

Kirillov, Oleg (2018) Classical Results and Modern Approaches to Nonconservative Stability. In: Dynamic Stability and Bifurcation in Nonconservative Mechanics. CISM International Centre for Mechanical Sciences, 586 (586). Springer, Berlin, pp. 129-190. ISBN 9783319937212

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

Bigoni, Davide and Kirillov, Oleg (2018) Dynamic Stability and Bifurcation in Nonconservative Mechanics. CISM International Centre for Mechanical Sciences, 586 . Springer. ISBN 978-3-319-93721-2

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

Kirillov, Oleg (2018) Locating the sets of exceptional points in dissipative systems and the self-stability of bicycles. Entropy, 20 (7). p. 502. ISSN 1099-4300

Bigoni, Davide, Tommasini, Mirko, Misseroni, Diego, Kirillov, Oleg and Noselli, Giovanni (2018) Flutter and divergence instability in the Pflüger column: Experimental evidence of the Ziegler destabilization paradox. Journal of the Mechanics and Physics of Solids, 116. pp. 99-116. ISSN 0022-5096

Ma, Youqiao, Guo, Di, Gao, Yangyuanlong, Sarah, Sabrina, Wu, Qiang, Zhou, Jun, Pistora, Jaromir and Cada, Michael (2018) High Sensitive Z-shaped Fiber Interferometric Refractive Index Sensor: Simulation and Experiment. IEEE Photonics Technology Letters, 30 (12). pp. 1131-1134. ISSN 1041-1135

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

Bigoni, Davide, Misseroni, Diego, Tommasini, Mirko, Kirillov, Oleg and Noselli, Giovanni (2018) Detecting singular weak-dissipation limit for flutter onset in reversible systems. Physical Review E (PRE), 97 (2). 023003. ISSN 2470-0045

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

Bigoni, Davide and Kirillov, Oleg (2018) Preface. In: Dynamic Stability and Bifurcation in Nonconservative Mechanics. CISM International Centre for Mechanical Sciences . Springer, v-vi. ISBN 978-3-319-93721-2

Bigoni, Davide, Misseroni, Diego, Tommasini, Mirko, Kirillov, Oleg and Noselli, Giovanni (2018) Detecting singular weak-dissipation limit for flutter onset in reversible systems. Physical Review E (PRE), 97 (2). 023003. ISSN 2470-0045


Kirillov, Oleg (2017) Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, 473 (2205). ISSN 1364-5021

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

Ablowitz, Mark, Ma, Yi-Ping and Rumanov, Igor (2017) A universal asymptotic regime in the hyperbolic nonlinear Schrodinger equation. SIAM Journal on Applied Mathematics, 77 (4). pp. 1248-1268. ISSN 0036-1399

Kirillov, Oleg, Stefani, Frank, Albrecht, Thomas, Arlt, Rainer, Christen, Michael, Gailitis, Agris, Gellert, Marcus, Giesecke, André, Goepfert, Oliver, Herault, Johann, Mamatsashvili, George, Priede, Janis, Rudiger, Guenther, Seilmayer, Martin, Tilgner, Andreas and Vogt, Tobias (2017) Magnetic field dynamos and magnetically triggered flow instabilities. IoP Conference Series, Materials Science and Engineering, 228 (1). 012002. ISSN 1757-8981

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

Kirillov, Oleg and Mutabazi, Innocent (2017) Short wavelength local instabilities of a circular Couette flow with radial temperature gradient. Journal of Fluid Mechanics, 818. pp. 319-343. ISSN 0022-1120

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

El, G.A., Hoefer, M.A. and M. Shearer, Dispersive and diffusive-dispersive shock waves for non-convex conservation laws, SIAM Review 59 (2017) 3-61.

Hoefer, M.A., El, G.A. and Kamchatnov, A.M., Oblique spatial dispersive shock waves in nonlinear Schrödinger flows, SIAM Journ. Appl. Math, 77 (2017) 1352 – 1374.

Suret, P., El, G., Onorato, M. and Randoux, S., Rogue Waves in Integrable Turbulence: Semi-Classical Theory and Fast Measurements, in: Guided wave optics: A testbed for extreme events, S. Wabnitz (ed.), IOP e-book (2017) pp. 12-1 -- 12-32, ISBN 978-0-7503-1460-2

Tikan, A, Billet, C., El, G., Tovbis, A., Bertola, M., Sylvestre, T., Gustave, F., Randoux, S., Genty, G., Suret, P., and Dudley, J., Universality of the Peregrine soliton in the focusing dynamics of the cubic nonlinear Schrödinger equation, Phys. Rev. Lett. 119 (2017) 033901 (Editors' Suggestion)

Chesnokov, A.A., El, G.A., Gavrilyuk, S.L. and Pavlov, M.V., Stability of shear shallow water flows with free surface, SIAM Journ Appl Math 77 (2017) 1068-1087.

Randoux, S., Gustave, F., Suret, P. and El, G., Optical random Riemann waves in integrable turbulence, Phys. Rev. Lett. 118 (2017) 233901.

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

Kirillov, Oleg and Levi, Mark (2017) A Coriolis force in an inertial frame. Nonlinearity, 30 (3). pp. 1109-1119. ISSN 0951-7715


Agliari, Elena, Barra, Adriano, Dello Schiavo, Lorenzo and Moro, Antonio (2016) Complete integrability of information processing by biochemical reactions. Scientific Reports, 6. p. 36314. ISSN 2045-2322

Ma, Yi-Ping and Knobloch, Edgar (2016) Two-dimensional localized structures in harmonically forced oscillatory systems. Physica D: Nonlinear Phenomena, 337. pp. 1-17. 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

Weidman, Patrick and Ma, Yi-Ping (2016) The competing effects of wall transpiration and stretching on Homann stagnation-point flow. European Journal of Mechanics - B/Fluids, 60. pp. 237-241. ISSN 0997-7546

Biondini, G., El, G.A., Hoefer, M. and Miller, P.D., Dispersive hydrodynamics: Preface, Physica D 333 (2016) 1-5.

El, G.A. and Hoefer, M.A. Dispersive shock waves and modulation theory, Physica D 333 (2016) 11 – 65 (Invited Review for the Special Issue on Dispersive Hydrodynamics).

Bertola, M., El, G.A. and Tovbis, A. Rogue waves in multiphase solutions of the focusing NLS equation, Proc. Roy. Soc. A 472 (2016) 20160340.

El, G.A., Khamis, E.G. and Tovbis, A., Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves, Nonlinearity 29 (2016) 2798 – 2836.

Onorato, M., Proment, D., El, G., Randoux, S. and Suret, P., On the origin of heavy-tail statistics in equations of Nonlinear Schrödinger type, Phys. Lett. A 380 (2016) 3173 – 3177.

Randoux, S., Suret, P. and El, G.A., Inverse scattering transform analysis of rogue waves using local periodization procedure, Sci. Rep. 6 (2016) 29238.

Tommasini, Mirko, Kirillov, Oleg, Misseroni, Diego and Bigoni, Davide (2016) The destabilizing effect of external damping: Singular flutter boundary for the Pflüger column with vanishing external dissipation. Journal of the Mechanics and Physics of Solids, 91. pp. 204-215. ISSN 0022-5096

El, G.A., Hoefer, M.A. and Shearer, M., Expansion shock waves in regularized shallow water theory, Proc. Roy. Soc. A 472 (2016) 20160141.

Tovbis, A. and El, G.A., Semi-classical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach, Physica D 333 (2016) 171 -184.

El, G.A. and Smyth, N.F., Radiating dispersive shock waves in nonlocal optical media, Proc. Roy. Soc. A 472 (2016) 20150633.

El, G.A., Critical density of a soliton gas, CHAOS 26 (2016) 023105.

Carbone, F., Dutykh, D. and El, G.A., Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modelling, Europhys. Lett., 113 (2016) 30003.

Ablowitz, Mark, Demirci, Ali and Ma, Yi-Ping (2016) Dispersive shock waves in the Kadomtsev–Petviashvili and two dimensional Benjamin–Ono equations. Physica D: Nonlinear Phenomena, 333. pp. 84-98. ISSN 0167-2789

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

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

Chong, Christopher, Kevrekidis, Panayotis, Ablowitz, Mark and Ma, Yi-Ping (2016) Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices. Physical Review E, 93 (1). 012909. ISSN 2470-0045

Kirillov, Oleg and Levi, Mark (2016) Rotating saddle trap as Foucault's pendulum. American Journal of Physics, 84 (1). pp. 26-31. ISSN 0002-9505


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

Stefani, Frank and Kirillov, Oleg (2015) Destabilization of rotating flows with positive shear by azimuthal magnetic fields. Physical Review E, 92 (5). 051001(R). ISSN 1539-3755

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

Ablowitz, Mark and Ma, Yi-Ping (2015) Strong transmission and reflection of edge modes in bounded photonic graphene. Optics Letters, 40 (20). p. 4635. ISSN 0146-9592

Ablowitz, Mark, Curtis, Christopher and Ma, Yi-Ping (2015) Adiabatic dynamics of edge waves in photonic graphene. 2D Materials, 2 (2). 024003. ISSN 2053-1583

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

Kirillov, Oleg, Stefani, F. and Fukumoto, Y. (2014) Local instabilities in magnetized rotational flows: a short-wavelength approach. Journal of Fluid Mechanics, 760. pp. 591-633. ISSN 0022-1120

Ablowitz, Mark, Curtis, Christopher and Ma, Yi-Ping (2014) Linear and nonlinear traveling edge waves in optical honeycomb lattices. Physical Review A, 90 (2). 023813. ISSN 1050-2947

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

Lerbet, Jean, Aldowaji, Marwa, Challamel, Noël, Kirillov, Oleg, Nicot, François and Darve, Félix (2014) Geometric degree of nonconservativity. Mathematics and Mechanics of Complex Systems, 2 (2). pp. 123-139. ISSN 2326-7186

Kirillov, Oleg, Stefani, Frank and Fukumoto, Yasuhide (2014) Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence. Fluid Dynamics Research, 46 (3). 031403. ISSN 0169-5983

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

Lowman, N.K., Hoefer, M.A., and El, G.A., Interactions of large-amplitude solitary waves in viscous fluid conduits, Journ. Fluid. Mech. 750 (2014) 372 – 384.

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

Kirillov, Oleg, Challamel, N., Darve, F., Lerbet, J. and Nicot, F. (2014) Singular divergence instability thresholds of kinematically constrained circulatory systems. Physics Letters A, 378 (3). pp. 147-152. ISSN 0375-9601

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