Professor Gennady El

Professor

School: Engineering, Physics and Mathematics

Gennady El's main research interests lie in the theory and applications of dispersive hydrodynamics---a mathematical theory of multiscale nonlinear wave phenomena in dispersive media, encompassing deterministic and stochastic aspects of wave propagation. G. El has extensively worked on modulation theory of dispersive shock waves in integrable and non-integrable systems with applications in water waves, nonlinear optcs and condensed matter physics. His current research at the intersection of integrable systems and statistical mechancs is concerned with various aspects of spectral theory of soliton and breather gases using the inverse scattering transform and the tools of generalised hydrodynamics combined with high accuracy numerical simulations. G.El is involved in close collaborations with experimentalists in fluids and fibre optics. He has also completed several projects with industrial partners.

Before joining in 2018 the Department of Mathematics, Physics and Electrical Engineering at Northumbria University as a Professor of Applied Mathematics G. El had held positions of a Lecturer, Senior Lecturer and Reader in Applied Mathematics at the Department of Mathematical Sciences, Loughborough University. In 2015-2020 he has been an Invited Professor at the Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), University of Lille, France. He currently holds Visiting Professorship at the Department of Mathematical Sciences, Loughborough University.

G. El is a member of the London Mathematical Society (LMS) and of the Society for Industrial and Applied Mathematics (SIAM). He is also a member of the SIAM Activity Group in Nonlinear Waves. G. El is co-founder and Deputy Editor of Journal of Nonlinear Waves, Cambridge University Press

Email Gennady

Research Themes and Scholarly Interests

Nonlinear dispersive waves; Solitons; Asymptotic methods for PDE's; Dispersive hydrodynamics; Fluid dynamics and nonlinear optics applications

Key Publications

Please visit the Pure Research Information Portal for further information
Exactly Solvable Model of Wave-Mean Field Interaction in Integrable Turbulence, Congy, T., El, G., Hoefer, M. 10 Apr 2026, In: Physical Review Letters
Soliton gas in optical fiber experiments: nonlinear Fourier transform of the noise-induced modulational instability, Lebel, A., Roberti, G., Randoux, S., Bonnemain, T., Copie, F., El, G., Suret, P. 6 Feb 2026, In: Journal of Nonlinear Waves
Breather gas fission from elliptic potentials in self-focusing media, Biondini, G., El, G., Luo, X., Oregero, J., Tovbis, A. 6 Jan 2025, In: Physical Review E
Dissipation-Driven Emergence of a Soliton Condensate in a Nonlinear Electrical Transmission Line, Fache, L., Damart, H., Copie, F., Bonnemain, T., Congy, T., Roberti, G., Suret, P., El, G., Randoux, S. 7 Apr 2025, In: Physical Review Letters
Experimental observation of the spatio-temporal dynamics of breather gases in a recirculating fiber loop, Copie, F., Biondini, G., Oregero, J., El, G., Suret, P., Randoux, S. 15 Nov 2025, In: Optics Letters
Riemann problem for polychromatic soliton gases: A testbed for the spectral kinetic theory, Congy, T., Carr, H., Roberti, G., El, G. 1 Apr 2025, In: Wave Motion
Solitary wave-mean flow interaction in strongly nonlinear dispersive shallow water waves, Congy, T., El, G., Gavrilyuk, S., Hoefer, M., Shyue, K. 8 Aug 2025, In: Journal of Nonlinear Waves
Spontaneous modulational instability of elliptic periodic waves: The soliton condensate model, Agafontsev, D., Congy, T., El, G., Randoux, S., Roberti, G., Suret, P. 1 Dec 2025, In: Physica D: Nonlinear Phenomena
Two-dimensional stationary soliton gas, Bonnemain, T., Biondini, G., Doyon, B., Roberti, G., El, G. 7 Feb 2025, In: Physical Review Research
Interaction of soliton gases in deep-water surface gravity waves, Fache, L., Bonnefoy, F., Ducrozet, G., Copie, F., Novkoski, F., Ricard, G., Roberti, G., Falcon, E., Suret, P., El, G., Randoux, S. 15 Mar 2024, In: Physical Review E

Current and Recent Projects

Please visit the Pure Research Information Portal for further information
Wave-mean field interaction in integrable turbulence, El, G. (Principal Investigator), Engineering and Physical Sciences Research Council, 01/02/26 - 31/01/27, £76,876.00
Emergent Phenomena in Nonlinear Dispersive Waves, El, G. (Principal Investigator), Isaac Newton Institute for Mathematical Sciences, 22/07/24 - 16/08/24, £110,169.00
Visiting Professorship -- Professor Mark Hoefer, El, G. (Principal Investigator), The Leverhulme Trust, 01/07/24 - 30/09/24, £26,005.00
Fuse Fibre Phase 3, El, G. (Principal Investigator), LumOptica Limited, 26/01/24 - 25/05/24, £28,000.00
Soliton gas at the crossroads of dispersive and generalised hydrodynamics, El, G. (Principal Investigator), Engineering and Physical Sciences Research Council, 01/04/22 - 31/03/23, £80,498.00
Riemann problem for the Benjamin-Bona-Mahony equation, El, G. (Principal Investigator), London Mathematical Society, 01/12/19 - 31/12/19, £1,000.00
Pulse Compression in Extremely Nonlinear Regimes, El, G. (Principal Investigator), LumOptica Limited, 01/08/19 - 31/05/20, £69,932.00
Nonlinear Photonics, Fibre Laser System, El, G. (Principal Investigator), Ministry of Defence (MoD), 01/10/18 - 30/09/20, £73,625.00
Integrable turbulence and rogue waves: semi-classical nonlinear Schrödinger equation framework, El, G. (Principal Investigator), Engineering and Physical Sciences Research Council, 01/09/18 - 31/10/20, £242,791.00