Kinetic equation for a dense soliton gas

G. A. El*, A. M. Kamchatnov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

97 Citations (Scopus)
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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.

Original languageEnglish
Article number204101
JournalPhysical Review Letters
Volume95
Issue number20
Early online date7 Nov 2005
DOIs
Publication statusPublished - 11 Nov 2005
Externally publishedYes

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