Multidimensional conservation laws and integrable systems II

In this paper we continue investigation of 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. Multicomponent two‐dimensional hydrodynamic reductions of the Mikhalëv equat...

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Bibliographic Details
Published in:Studies in applied mathematics (Cambridge) 2022-02, Vol.148 (2), p.813-824
Main Authors: Makridin, Zakhar V., Pavlov, Maxim V.
Format: Article
Language:English
Subjects:
Commuting
Conservation laws
integrable system
Korteweg–de Vries equation
Mikhalëv equation
multidimensional conservation laws
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Summary:In this paper we continue investigation of 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. Multicomponent two‐dimensional hydrodynamic reductions of the Mikhalëv equation are considered. Infinitely many three‐dimensional local conservation laws for the Korteweg–de Vries pair of commuting flows are constructed. Thus, we show that pairs of commuting dispersive two‐dimensional systems also possess infinitely many local three‐dimensional conservation laws. They can be used for averaging of multiparametric families of solutions to the Mikhalëv equation.
ISSN:0022-2526
1467-9590
DOI:10.1111/sapm.12460