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Frobenius integrable decompositions of nonlinear evolution equations with modified term. (English) Zbl 1364.35073

Summary: Frobenius integrable decompositions are introduced for nonlinear evolution equations with modified term. Two classes of polynomial equations with modified term are transformed into Frobenius integrable ordinary differential equations by two special Bäcklund transformations. The resulting solutions are illustrated to describe the solution phenomena shared with the mKdV equation, Sharma-Tasso-Olver equation, the modified Kawachara equation, the fifth-order KdV equation and its various forms.

MSC:

35G20 Nonlinear higher-order PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
35Q53 KdV equations (Korteweg-de Vries equations)
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