Kinetic equation for a soliton gas and its hydrodynamic reductions

G. A. El, A. M. Kamchatnov, M. V. Pavlov, S. A. Zykov

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)
4 Downloads (Pure)


We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N-component 'cold-gas' hydrodynamic reductions. We prove that these reductions represent integrable linearly degenerate hydrodynamic type systems for arbitrary N which is a strong evidence in favour of integrability of the full kinetic equation. We derive compact explicit representations for the Riemann invariants and characteristic velocities of the hydrodynamic reductions in terms of the 'cold-gas' component densities and construct a number of exact solutions having special properties (quasiperiodic, self-similar). Hydrodynamic symmetries are then derived and investigated. The obtained results shed light on the structure of a continuum limit for a large class of integrable systems of hydrodynamic type and are also relevant to the description of turbulent motion in conservative compressible flows.

Original languageEnglish
Pages (from-to)151-191
Number of pages41
JournalJournal of Nonlinear Science
Issue number2
Early online date17 Sept 2010
Publication statusPublished - 1 Apr 2011
Externally publishedYes


Dive into the research topics of 'Kinetic equation for a soliton gas and its hydrodynamic reductions'. Together they form a unique fingerprint.

Cite this