1992•Journal of Physics A Mathematical and GeneralOpen access

Reductions of (2+1)-dimensional integrable systems via mixed potential-eigenfunction constraints

Boris Georgievich Konopelchenko, Walter Strampp

Abstract

New types of reductions of (2+1)-dimensional integrable systems which are associated with mixed potential-eigenfunction constraints are discussed. Necessary and sufficient conditions for the admissibility of such constraints are presented. Classification results for integrable equations will be used for applying these conditions. Several typical examples are considered, including the KP, mKP, (2+1)-dimensional Savada-Kotera-Kaup-Kupershmidt, Harry Dym and Nizhnik-Veselov-Novikov equations.

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Key concepts: Integrable system, Eigenfunction, Mathematics, Novikov self-consistency principle, Applied mathematics, Mathematical analysis, Pure mathematics, Eigenvalues and eigenvectors