Prof. Gennady El - Soliton gas in integrable dispersive hydrodynamics

Soliton gas can be viewed as an infinite random ensemble of interacting solitons displaying a nontrivial collective, hydrodynamic behaviour, ultimately determined by the properties of elementary two-soliton nonlinear interactions. More generally, the emergence at large scales of a rich, sometimes counter-intuitive, phenomenology from otherwise simple microscopic interactions in complex systems is at the forefront of contemporary mathematical and theoretical physics.   Recent theoretical and experimental research has shown that soliton gas dynamics in integrable systems such as the Korteweg-de Vries and nonlinear Schrodinger equations are instrumental in the understanding of  a number of fundamental physical phenomena such as spontaneous modulation instability and the formation of rogue waves. In my talk I will review  nonlinear spectral  theory of soliton gas and its relation with the ideas of "integrable turbulence". Physical experiments on the soliton gas generation in water waves will be discussed.

[1] G.A. El, Soliton gas in integrable dispersive hydrodynamics, Journal of Statistical Mechanics: Theory and Experiment (2021) 114001.

[2] A. Gelash, D. Agafontsev, V. Zakharov, G. El, S. Randoux, and P. Suret, Bound state soliton gas dynamics underlying the spontaneous modulational instability, Phys. Rev. Lett. 123 (2019) 234102.

[3] G. El and A. Tovbis, Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation, Phys. Rev. E, 101 (2020) 052207.