This article is cited in 5 papers

Symmetrical polynomials and conservation laws

A. B. Shabat<sup>ab

a</sup> Landau Institute for Theoretical Physics, Russian Academy of Sciences, Russia, Chernogolovka
^b Karachay-Cherkess State University, Russia, Karachaevsk

Abstract: Vector fields with symmetrical polynomials as the first integrals are considered. The connection of these dynamical systems with the theory of multi-phase solutions of the solitonic models of mathematical physics is established.

Key words: Liouville therem, symmetric polynomials, Riemann invariants, solitonic equations.

UDC: 517.928

Received: 30.11.2012