One World Waves Gennady El - Modulational instability and nonlinear spectral theory of soliton gas
From OLLIE Quinn on November 5th, 2020
Solitons are localised solutions of integrable systems that can be viewed as “particles” of complex statistical objects called soliton gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media, such “integrable” gases are of fundamental interest for nonlinear physics. In particular, it has been shown recently (PRL 123, 234102 (2019)) that the long-time asymptotic behaviour of the noise-induced, spontaneous modulational instability can be accurately modelled by certain dense soliton gas dynamics. In my talk, I will outline nonlinear spectral theory of soliton gases based on a special, thermodynamic-type limit of multiphase (finite-gap) solutions and their modulations for the focusing nonlinear Schrödinger equation (PRE 101, 052207 (2020), joint with A. Tovbis). Wherever possible, connections with physical experiments will be highlighted.