Abstract

We analyze various integrable dispersive equations when the number of solitons goes to infinity and we call this kind of solutions a deterministic soliton  gas.We then analyze the behaviour of a single soliton interacting with a soliton gas.We are able to derive the kinetic velocity equations and the local phase shift of the gasafter the passage of the soliton, and we can trace the location of the soliton peak as the dynamicsevolves.Based on 

Girotti, M.; Grava, T.; Jenkins, R.; McLaughlin, K. D. T.-R. Rigorous asymptotics of a KdV soliton gas. Comm. Math. Phys. 384 (2021), no. 2, 733–784. Girotti, M.; Grava, T.; Jenkins, R.; McLaughlin, K. D. T.-R.   Soliton v. the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation.\\ Preprint  https://arxiv.org/pdf/2205.02601.pdf Bertola,  M.; Grava, T.; Orsatti, G. Soliton shielding of the focusing nonlinear Schrodinger equation. Preprint  https://arxiv.org/pdf/2112.05985.pdf