TY - JOUR

T1 - Multi-dimensional conservation laws and integrable systems

AU - Makridin, Zakhar V.

AU - Pavlov, Maxim V.

N1 - Publisher Copyright: © 2019 Wiley Periodicals, Inc., A Wiley Company Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/11

Y1 - 2019/11

N2 - 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.

AB - 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.

KW - dispersionless limit of the Kadomtsev-Petviashvili equation

KW - integrable system

KW - multi-dimensional conservation laws

KW - the Benney hydrodynamic chain

KW - then Mikhalëv equation

KW - GEOMETRIC APPROACH

KW - WAVES

KW - EQUATIONS

KW - then Mikhalev equation

UR - http://www.scopus.com/inward/record.url?scp=85070856503&partnerID=8YFLogxK

U2 - 10.1111/sapm.12280

DO - 10.1111/sapm.12280

M3 - Article

AN - SCOPUS:85070856503

VL - 143

SP - 339

EP - 355

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 4

ER -