This article is cited in 3 papers

An effective algorithm for finding multidimensional conservation laws for integrable systems of hydrodynamic type

Z. V. Makridin<sup>ab

a</sup> Novosibirsk State University, Novosibirsk, Russia
^b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We study a new property of integrable systems, the existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional hydrodynamic chains. We describe an effective algorithm for successively computing an infinite set of three-dimensional conservation laws for the Benney pair of commuting flows.

Keywords: integrable system, overdetermined system, hydrodynamic Benney chain, Kadomtsev–Petviashvili equation, three-dimensional conservation law.

Received: 20.04.2017

DOI: 10.4213/tmf9385

 English version: Theoretical and Mathematical Physics, 2018, 194:2, 274–283

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