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

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