Kinetic Equation for a Dense Soliton Gas

El, Gennady and Kamchatnov, A. M. (2005) Kinetic Equation for a Dense Soliton Gas. Physical Review Letters, 95 (20). p. 204101. ISSN 0031-9007

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Official URL: https://doi.org/10.1103/PhysRevLett.95.204101

Abstract

We propose a general method to derive kinetic equations for dense soliton gases in physical systems described by integrable nonlinear wave equations. The kinetic equation describes evolution of the spectral distribution function of solitons due to soliton-soliton collisions. Owing to complete integrability of the soliton equations, only pairwise soliton interactions contribute to the solution, and the evolution reduces to a transport of the eigenvalues of the associated spectral problem with the corresponding soliton velocities modified by the collisions. The proposed general procedure of the derivation of the kinetic equation is illustrated by the examples of the Korteweg-de Vries and nonlinear Schrödinger (NLS) equations. As a simple physical example, we construct an explicit solution for the case of interaction of two cold NLS soliton gases.

Item Type: Article
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: John Coen
Date Deposited: 16 Apr 2020 10:29
Last Modified: 16 Apr 2020 10:30
URI: http://nrl.northumbria.ac.uk/id/eprint/42799

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