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 crossfertilisation between different research areas and disciplines.
Complexity and nonlinearity are often concomitant features of realworld 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 crossfertilisation between different research areas and disciplines.
Northumbria's MCNP Research Group conducts interdisciplinary research aiming at impacting on challenges posed by a fastchanging world. It is engaged in groundbreaking 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 Goussev  Dr Thibault Congy  Marta dell'Atti 
Dr Benoit Huard  David Graham  
Dr Oleg Kirillov  Joris Labarbe  
Dr Yiping Ma  Giacomo Roberti  
Dr Antonio Moro  Marzia Romano  
Dr Matteo Sommacal  Oleg Senkevich  
David Snee 
Dr Costanza Benassi  


Dr Thibault Congy  
Personal page: https://tcongy.github.io/ 

Prof Gennady El  
Funding: EPSRC (20172010, Grant No. EP/R00515X/1); Dstl (20172020, Contract No DSTLX1000116851); LMS Research in Pairs Grants (2014, 2015, 2017, 2018), the Royal Society International Exchanges Scheme (20142016). Full details in the Dispersive Hydrodynamics page. 

Dr Arseni Goussev  
Personal page: https://sites.google.com/site/aogscifi 

Dr Benoit Huard  


Dr Yiping Ma  


Dr Antonio Moro  
Nonlinear Conservation laws and applications
For more details click here. 

Dr Matteo Sommacal  

Current

Adam Bridgewater (October 2015December 2018). Principal supervisor B. Huard.
Mathematical description of oscillatory regimes in the glucoseinsulin regulation

Marta dell'Atti. Principal supervisor A. Moro.

David Graham. Principal supervisor A. Moro.

Joris Labarbe (October 2018 ). Principal supervisor O. Kirillov.

Giacomo Roberti (October 2018 ). Principal supervisor G. El.
Analysis and control of largeamplitude fluctuations of incoherent optical field in fibre lasers: integrable turbulence framework

Marzia Romano (to be submitted, December 2018March 2019). Principal supervisor M. Sommacal.
The 3wave resonant interaction model: spectra and instabilities of plane waves

Oleg Senkevich. Principal supervisor A. Moro.

David Snee. Principal supervisor Y. Ma.
Nonlinear edge waves in mechanical topological insulators

Maximilien Barbier (February 2017). Principal supervisor A. Goussev.
Dynamics of matter wave packets in the presence of timedependent absorption

Francesco Giglio (February 2018). Principal supervisor A. Moro.
Wave dynamics and catastrophes in thermodynamic phase diagrams

Emrah Haspolat (February 2018). Principal supervisor B. Huard.
Mathematical modelling of Arabidopsis flowering time gene regulatory network
The group runs the weekly Mathematics and Mathematical Physics series of research seminars and colloquia. Full details can be found at the seminars page.
2018
Kirillov, Oleg (2018) DissipationInduced Instabilities in Magnetized Flows. Journal of Mathematical Sciences. ISSN 10723374 (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 00222526 (In Press)
Haspolat, Emrah, Huard, Benoit and Angelova, Maia (2018) Deterministic and stochastic models of Arabidopsis Thaliana flowering. Bulletin of Mathematical Biology. ISSN 00928240 (In Press)
Demontis, Francesco, Lombardo, Sara, Sommacal, Matteo, van der Mee, Cornelis and Vargiu, F. (2018) Effective generation of closedform soliton solutions of the continuous classical Heisenberg ferromagnet equation. Communications in Nonlinear Science and Numerical Simulation, 64. pp. 3565. ISSN 10075704
De Matteis, Giovanni, Giglio, Francesco and Moro, Antonio (2018) Exact equations of state for nematics. Annals of Physics, 396. pp. 386396. ISSN 00034916
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 24700045
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. 129190. ISBN 9783319937212
Degasperis, Antonio, Lombardo, Sara and Sommacal, Matteo (2018) Integrability and linear stability of nonlinear waves. Journal of Nonlinear Science, 28 (4). pp. 12511291. ISSN 09388974
Bigoni, Davide and Kirillov, Oleg (2018) Dynamic Stability and Bifurcation in Nonconservative Mechanics. CISM International Centre for Mechanical Sciences, 586 . Springer. ISBN 9783319937212
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 24699926
Kirillov, Oleg (2018) Locating the sets of exceptional points in dissipative systems and the selfstability of bicycles. Entropy, 20 (7). p. 502. ISSN 10994300
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. 99116. ISSN 00225096
Ma, Youqiao, Guo, Di, Gao, Yangyuanlong, Sarah, Sabrina, Wu, Qiang, Zhou, Jun, Pistora, Jaromir and Cada, Michael (2018) High Sensitive Zshaped Fiber Interferometric Refractive Index Sensor: Simulation and Experiment. IEEE Photonics Technology Letters, 30 (12). pp. 11311134. ISSN 10411135
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. 134. ISSN 10726691
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 00319007
Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2018) The continuous classical Heisenberg ferromagnet equation with inplane asymptotic conditions. II. IST and closedform soliton solutions. Ricerche di Matematica. ISSN 00355038 (In Press)
Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo and van der Mee, Cornelis (2018) The continuous classical Heisenberg ferromagnet equation with inplane asymptotic conditions. I. Direct and inverse scattering theory. Ricerche di Matematica. ISSN 00355038 (In Press)
Sprenger, Patrick, Hoefer, Mark and El, Gennady (2018) Hydrodynamic optical soliton tunneling. Physical Review E, 97 (3). ISSN 24700045
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 13672630
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. 13921416. ISSN 09517715
Bigoni, Davide, Misseroni, Diego, Tommasini, Mirko, Kirillov, Oleg and Noselli, Giovanni (2018) Detecting singular weakdissipation limit for flutter onset in reversible systems. Physical Review E (PRE), 97 (2). 023003. ISSN 24700045
El, Gennady, Hoefer, Mark A. and Shearer, Michael (2018) Stationary Expansion Shocks for a Regularized Boussinesq System. Studies in Applied Mathematics, 140 (1). pp. 2747. ISSN 00222526
Bigoni, Davide and Kirillov, Oleg (2018) Preface. In: Dynamic Stability and Bifurcation in Nonconservative Mechanics. CISM International Centre for Mechanical Sciences . Springer, vvi. ISBN 9783319937212
Bigoni, Davide, Misseroni, Diego, Tommasini, Mirko, Kirillov, Oleg and Noselli, Giovanni (2018) Detecting singular weakdissipation limit for flutter onset in reversible systems. Physical Review E (PRE), 97 (2). 023003. ISSN 24700045
2017Kirillov, Oleg (2017) Singular diffusionless limits of doublediffusive instabilities in magnetohydrodynamics. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences, 473 (2205). ISSN 13645021
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 17518113
Ablowitz, Mark, Ma, YiPing and Rumanov, Igor (2017) A universal asymptotic regime in the hyperbolic nonlinear Schrodinger equation. SIAM Journal on Applied Mathematics, 77 (4). pp. 12481268. ISSN 00361399
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 17578981
Goussev, Arseni (2017) Rotating Gaussian wave packets in weak external potentials. Physical Review A (PRA), 96. 013617. ISSN 10502947
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. 319343. ISSN 00221120
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 24699950
El, G.A., Hoefer, M.A. and M. Shearer, Dispersive and diffusivedispersive shock waves for nonconvex conservation laws, SIAM Review 59 (2017) 361.
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: SemiClassical Theory and Fast Measurements, in: Guided wave optics: A testbed for extreme events, S. Wabnitz (ed.), IOP ebook (2017) pp. 121  1232, ISBN 9780750314602
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) 10681087.
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 glucoseinsulin regulation. Journal of Theoretical Biology, 418. pp. 6676. ISSN 00225193
Kirillov, Oleg and Levi, Mark (2017) A Coriolis force in an inertial frame. Nonlinearity, 30 (3). pp. 11091119. ISSN 09517715
2016Agliari, Elena, Barra, Adriano, Dello Schiavo, Lorenzo and Moro, Antonio (2016) Complete integrability of information processing by biochemical reactions. Scientific Reports, 6. p. 36314. ISSN 20452322
Ma, YiPing and Knobloch, Edgar (2016) Twodimensional localized structures in harmonically forced oscillatory systems. Physica D: Nonlinear Phenomena, 337. pp. 117. ISSN 01672789
Giglio, Francesco, Landolfi, Giulio and Moro, Antonio (2016) Integrable extended van der Waals model. Physica D: Nonlinear Phenomena, 333. pp. 293300. ISSN 01672789
Weidman, Patrick and Ma, YiPing (2016) The competing effects of wall transpiration and stretching on Homann stagnationpoint flow. European Journal of Mechanics  B/Fluids, 60. pp. 237241. ISSN 09977546
Biondini, G., El, G.A., Hoefer, M. and Miller, P.D., Dispersive hydrodynamics: Preface, Physica D 333 (2016) 15.
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 heavytail 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. 204215. ISSN 00225096
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., Semiclassical limit of the focusing NLS: Whitham equations and the RiemannHilbert 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: solitongas kinetics and direct numerical modelling, Europhys. Lett., 113 (2016) 30003.
Ablowitz, Mark, Demirci, Ali and Ma, YiPing (2016) Dispersive shock waves in the Kadomtsev–Petviashvili and two dimensional Benjamin–Ono equations. Physica D: Nonlinear Phenomena, 333. pp. 8498. ISSN 01672789
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 1364503X
Goussev, Arseni, Robbins, Jonathan, Slastikov, Valeriy and Tretiakov, Oleg (2016) DzyaloshinskiiMoriya domain walls in magnetic nanotubes. Physical Review B (PRB), 93 (5). 054418. ISSN 10980121
Chong, Christopher, Kevrekidis, Panayotis, Ablowitz, Mark and Ma, YiPing (2016) Conical wave propagation and diffraction in twodimensional hexagonally packed granular lattices. Physical Review E, 93 (1). 012909. ISSN 24700045
Kirillov, Oleg and Levi, Mark (2016) Rotating saddle trap as Foucault's pendulum. American Journal of Physics, 84 (1). pp. 2631. ISSN 00029505
2015Barbier, Maximilien, Beau, Mathieu and Goussev, Arseni (2015) Comparison between two models of absorption of matter waves by a thin timedependent barrier. Physical Review A (PRA), 92 (053630). ISSN 10502947
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 15393755
Huard, Benoit, Easton, Jonathan and Angelova, Maia (2015) Investigation of stability in a twodelay model of the ultradian oscillations in glucoseinsulin regulation. Communications in Nonlinear Science and Numerical Simulation, 26 (13). pp. 211222. ISSN 10075704
Ablowitz, Mark and Ma, YiPing (2015) Strong transmission and reflection of edge modes in bounded photonic graphene. Optics Letters, 40 (20). p. 4635. ISSN 01469592
Ablowitz, Mark, Curtis, Christopher and Ma, YiPing (2015) Adiabatic dynamics of edge waves in photonic graphene. 2D Materials, 2 (2). 024003. ISSN 20531583
Barra, Adriano and Moro, Antonio (2015) Exact solution of the van der Waals model in the critical region. Annals of Physics, 359. pp. 290299. ISSN 00034916
Arsie, Alessandro, Lorenzoni, Paolo and Moro, Antonio (2015) Integrable viscous conservation laws. Nonlinearity, 28 (6). pp. 18591895. ISSN 09517715
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. 631707. ISSN 09388974
Goussev, Arseni (2015) Manipulating quantum wave packets via timedependent absorption. Physical Review A (PRA), 91 (4). 043638. ISSN 10502947
2014Barra, 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 14712946
Kirillov, Oleg, Stefani, F. and Fukumoto, Y. (2014) Local instabilities in magnetized rotational flows: a shortwavelength approach. Journal of Fluid Mechanics, 760. pp. 591633. ISSN 00221120
Ablowitz, Mark, Curtis, Christopher and Ma, YiPing (2014) Linear and nonlinear traveling edge waves in optical honeycomb lattices. Physical Review A, 90 (2). 023813. ISSN 10502947
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 14712946
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. 123139. ISSN 23267186
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 01695983
Moro, Antonio (2014) Shock dynamics of phase diagrams. Annals of Physics, 343. pp. 4960. ISSN 00034916
Goussev, Arseni, Robbins, Jonathan and Slastikov, Valeriy (2014) Domain wall motion in thin ferromagnetic nanotubes: Analytic results. Europhysics Letters, 105 (6). p. 67006. ISSN 02955075
Dubertrand, Remy and Goussev, Arseni (2014) Origin of the exponential decay of the Loschmidt echo in integrable systems. Physical Review E, 89. 022915. ISSN 15393755
Lowman, N.K., Hoefer, M.A., and El, G.A., Interactions of largeamplitude 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 15502376
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. 147152. ISSN 03759601
Forthcoming

3rd IMA Conference on Nonlinearity and Coherent Structures, 1012 July 2019 (Supported by the IMA).

Integrable Systems in Newcastle, 56 April 2019 (Supported by the LMS).

Mathematics of Biological Rhythms, 35 December 2018 (Supported by the Academy of Medical Sciences).
 London Mathematical Society Northern Regional Meeting, 2325 May 2018 (Supported by the LMS).