Mathematical Sciences

Department staff

Professor Gennady El

Photo of Professor  Gennady El

2010 - present: Reader in Applied Mathematics, Department of Mathematical Sciences, Loughborough University

2008 - 2010: Senior Lecturer, Department of Mathematical Sciences, Loughborough University.

2005 - 2008: Lecturer, Department of Mathematical Sciences, Loughborough University.

2000 - 2005: Leading Research Scientist, Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, Moscow, Russia.

1991 - 2000: Junior Research Scientist, Research Scientist, then Senior Research Scientist, Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, Moscow, Russia

1987 - 1991: Postgraduate, Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation (IZMIRAN), Russian Academy of Sciences, Moscow, Russia. PhD in Theoretical Physics.

1980 - 1986: Department of Physics and Mechanics, St. Petersburg Polytechnic University, Russia. MSc in Physics and Engineering.

Nonlinear Dispersive Waves: Theory and Applications

  • solitons and dispersive shock waves in integrable and non-integrable systems
  • Whitham modulation theory
  • asymptotics for nonlinear PDEs
  • random nonlinear dispersive waves
  • integrable turbulence
  • shallow-water waves and undular bores
  • interactions of dispersive-hydrodynamic flows with obstacles
  • fibre optics communications
  • ocean dynamics and rogue waves
  • hydrodynamic effects in optics and cold atom physics

Current funding:

  • 2017-2020: EPSRC Standard Research Grant No EP/R00515X/1. Project title: “Integrable turbulence and rogue waves: semi-classical nonlinear Schrödinger equation framework”.
  • 2017-2020: DSTL Grant Grant . Project title: “Analysis and control of large-amplitude fluctuations of incoherent optical field in fibre lasers: integrable turbulence framework”.

External activities:

  • Guest Editor for the special issue of PHYSICA D on Dispersive Hydrodynamics dedicated to G.B. Whitham (Physica D 233 (2016))
  • Invited plenary talks and mini-courses (recent):
    • 2017: Summer School “Dispersive Hydrodynamics and Oceanography: from Experiments to Theory”, Les Houches, France. Plenary talk.
    • 2016: International Workshop “Mathematical Hydrodynamics”, Novosibirsk University, Russia. Invited mini-course.
    • 2015: BIRS Workshop “Dispersive Hydrodynamics: Mathematics of Dispersive Shock waves and Applications”, Banff, Canada. Keynote talk.
    • 2014: Invited lecture course at Lille 1 University, France.
    • 2013: 8th IMACS conference on Nonlinear Evolution Equations and Wave Phenomena, University of Georgia, Athens, US. Invited tutorial.
    • 2013: International Conference: “Nonlinear Optical and Atomic Systems: Deterministic and Stochastic Aspects”, CEMPI, University of Lille 1, France. Plenary talk.
    • 2013: International Workshop “Dispersive shocks: tidal waves, tidal waves and superfluids” CIRM, Marceille, France, Invited mini-course.
    • 2012: International School/Workshop “Dispersive Shocks”, SISSA, Trieste, Italy. Invited mini-course. 
  • Invited Colloquia
    • 2017: Department of Applied Mathematics, Colorado University, Boulder
    • 2015: Department of Mathematics, University of Central Florida, Orlando

Awards (recent)

  • 2014 - 2017: Invited Professorship, University of Science and Technology Lille 1, France.
  • 2016: Project Coordinator Award from IMeRA (Institute for Advanced Studies, Aix Marseille University, France) 


Research Coordinator and REF Champion for the Department of Mathematical Sciences


  • MAC251: Vibrations and Waves
  • MAD202: Nonlinear Waves (0.5)
  • MAGIC PGR course “Nonlinear Waves” (0.5)

Google Scholar         Research Gate           ORCID

Review Articles:

  • El, G.A., Hoefer, M.A. and Shearer,M.  Dispersive and diffusive-dispersive shock waves for non-convex conservation laws, SIAM Review 59 (2017) 3-61.
  • El, G.A. and Hoefer, M.A. Dispersive shock waves and modulation theory, Physica D 333 (2016) 11 – 65
  • El, G.A., Resolution of a shock in hyperbolic systems modified by weak dispersion, CHAOS, 15 (2005) Art No 037103

Recent Papers:

  • El, G.A., Hoefer, M.A. and Shearer, M., Stationary expansion shock waves for a regularized Boussinesq system, Studies in Applied Mathematics, 139 (2017) DOI: 10.1111/sapm.12191.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.