The \(K(m, n)\) equation with generalized evolution term studied by symmetry reductions and qualitative analysis. (English) Zbl 1246.35172

Summary: The authors obtain symmetry reductions of the \(K(m, n)\) equation with generalized evolution term. The reduction to ordinary differential equations comes from an optimal system of subalgebras. Some of these equations admit symmetries which lead to further reductions, and one of them comes out suitable for qualitative analysis. Its dynamical behavior is fully described and conservative quantities are stated.


35Q51 Soliton equations
35B06 Symmetries, invariants, etc. in context of PDEs
35A24 Methods of ordinary differential equations applied to PDEs
34A05 Explicit solutions, first integrals of ordinary differential equations
Full Text: DOI


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