Multi-Dimensional Conservation Laws and Integrable Systems
Abstract
In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many three-dimensional local conservation laws for the Korteweg de Vries pair of commuting flows and for the Benney commuting hydrodynamic chains are constructed. As a by-product we established a new method for computation of local conservation laws for three-dimensional integrable systems. The Mikhalev equation and the dispersionless limit of the Kadomtsev--Petviashvili equation are investigated. All known local and infinitely many new quasi-local three-dimensional conservation laws are presented. Also four-dimensional conservation laws are considered for couples of three-dimensional integrable quasilinear systems and for triples of corresponding hydrodynamic chains.
Cite
@article{arxiv.1704.04005,
title = {Multi-Dimensional Conservation Laws and Integrable Systems},
author = {Zakhar V. Makridin and Maxim V. Pavlov},
journal= {arXiv preprint arXiv:1704.04005},
year = {2017}
}