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Gennady El

Professor of Applied Mathematics

Department: Mathematics, Physics and Electrical Engineering

Gennady El 

I graduated from the Department of Physics and Mechanics of the Leningrad Polytechnic Institute (now St. Petersburg Polytechnic University) in 1986. I then moved to Moscow to work on a PhD project on nonlinear waves in plasma at the Lebedev Physical Institute, Russian Academy of Sciences. After obtaining a PhD in Theoretical Physics in 1991 I have held the posts of Researcher (1991-1993), Senior Researcher (1994 – 1999) and Leading Researcher (2000 – 2005) at the Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Moscow and also had visiting research fellowships at the Max Planck Institute for Solar System Research, Germany (1993 – 1995); Duke University, USA (1998); Monash University, Australia (1998 – 2000), and Coventry University, UK (2001 – 2005). In 2005 -2018 I have worked at Department of Mathematical Sciences, Loughborough University as a Lecturer (2005-2008), Senior Lecturer (2008 -2010), and a Reader in Applied Mathematics (2010 -2018).

In September 2018 I joined the Department of Mathematics, Physics and Electrical Engineering at Northumbria University as a Professor of Applied Mathematics. I am also a Visiting Professor at the Department of Mathematical Sciences, Loughborough University (2018 – present) and an Invited Professor at the Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), University of Lille, France (2015 – present)

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Research Themes & Scholarly Interests

I am an applied mathematician with broad interests in nonlinear waves, integrable systems, fluid mechanics and nonlinear optics. I am particularly interested in the mathematics of dispersive hydrodynamic phenomena including dispersive shock waves, soliton gases and extreme events such as rogue waves. My research is often motivated by physical applications and involves solving nonlinear partial differential equations using exact, asymptotic and numerical methods.

My current research interests include:

  • solitons and dispersive shock waves in integrable and non-integrable systems
  • multi-scale asymptotics and singular limits for nonlinear dispersive PDEs
  • Whitham modulation theory
  • nonlinear theory of modulational instability and rogue waves
  • random nonlinear dispersive waves, integrable turbulence and soliton gases
  • applications to water waves and nonlinear optics

Professional Activity

I am an ordinary member of the London Mathematical Society and a Fellow of the Higher Education Academy. I have been a member of Organising and Scientific Committees of a number of major international conferences and workshops including the BIRS workshop “Dispersive Hydrodynamics: Mathematics of Dispersive Shock Waves and Applications” (2015, Banff, Canada) and Dynamics Days Europe (2018, Loughborough). I was a Guest Editor of the Special Issue “Dispersive Hydrodynamics” of Physica D (2016, v. 333) dedicated to the memory of G.B. Whitham. I am a member of the Management Committee of the Centre for Nonlinear Mathematics and Applications at the Department of Mathematical Sciences, Loughborough University

Sponsors & Collaborators

My research is supported by various funding bodies including EPSRC (EP/D077559/1, EP/E040160/1, EP/R00515X/1), the Royal Society, the London Mathematical Society, and Dstl. I collaborate with the Dispersive Hydrodynamics Laboratory (DHL) at the University of Colorado Boulder and Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM) at Lille University. 

Current/Recent Projects

  • Integrable turbulence and rogue waves: semi-classical nonlinear Schrödinger equation framework, EPSRC grant EP/R00515X/1 (2017-2020), PI
  • Analysis and control of large-amplitude fluctuations of incoherent optical field in fibre lasers: integrable turbulence framework, Defence Science and Technology Laboratory (Dstl) grant (2017-2020), PI
  • Integrability of non-strictly hyperbolic conservation laws in dispersive hydrodynamics, Foundation IMéRA, France (2017), PI
  • Dispersive regularisation of non-convex hyperbolic conservation laws, the Royal Society International Exchanges Scheme Grant (2014-2016), PI
  • Isospectral kinetic equation for solitons: integrability, exact solutions and physical applications, EPSRC grant EP/E040160/1 (2007), PI
  • Generation of spatial dispersive shock waves in supersonic flow of Bose-Einstein condensate, EPSRC grant EP/D077559/1 (2006), PI
  • 15 smaller grants from IMA, the Royal Society and the London Mathematical Society (2004 – 2018), PI;
  • Named researcher in several NSF grants on dispersive hydrodynamics and hyperbolic conservation laws (2014 – 2021). Collaborations with M. Hoefer (University of Colorado, Boulder) and M. Shearer (North Carolina State University).

Key Publications/Outputs

  • M.D. Maiden, D.V. Anderson, N.A. Franco, G.A. El, and M.A. Hoefer, Solitonic dispersive hydrodynamics: theory and observation, Phys. Rev. Lett. 120 (2018) 144101.
  • G.A. El, M.A. Hoefer, and M. Shearer, Dispersive and diffusive-dispersive shock waves for non-convex conservation laws, SIAM Review 59 (2017) 3-61.
  • S. Randoux, F. Gustave, P. Suret, and G. El, Optical random Riemann waves in integrable turbulence, Phys. Rev. Lett. 118 (2017) 233901.
  • G.A. El, E.G. Khamis, and A. Tovbis, Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves, Nonlinearity 29 (2016) 2798 – 2836.
  • G.A. El, R.H.J. Grimshaw and W.K. Tiong, Transformation of a shoaling undular bore, J. Fluid Mech. 709 (2012) 371-395.
  • G.A. El, A.M. Kamchatnov, M.V. Pavlov,  and S.A. Zykov, Kinetic equation for a soliton gas and its hydrodynamic reductions, J. Nonlin. Sci. 21 (2011) 151-191.

PGR Supervision


G. Roberti (started 2017)


Past completions:

R. Clift (2012-2015)

W.K. Tiong (2010 - 2012)

A. Leszczyszyn (2007 - 2010)

A. Tyurina (2001 - 2004)


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