Multi-dimensional conservation laws and integrable systems

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Abstract

In this paper, we introduce a new property of two-dimensional integrable hydrodynamic chains—existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many local three-dimensional conservation laws 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 Mikhalëv equation and the dispersionless limit of the Kadomtsev-Petviashvili equation are investigated. All known local and infinitely many new quasilocal three-dimensional conservation laws are presented. Also four-dimensional conservation laws are considered for couples of three-dimensional integrable quasilinear systems and for triplets of corresponding hydrodynamic chains.

Original languageEnglish
Pages (from-to)339-355
Number of pages17
JournalStudies in Applied Mathematics
Volume143
Issue number4
DOIs
Publication statusPublished - Nov 2019

Keywords

  • dispersionless limit of the Kadomtsev-Petviashvili equation
  • integrable system
  • multi-dimensional conservation laws
  • the Benney hydrodynamic chain
  • then Mikhalëv equation
  • GEOMETRIC APPROACH
  • WAVES
  • EQUATIONS
  • then Mikhalev equation

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