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.
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- 1.01 МАТЕМАТИКА