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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.
35Q51Soliton-like equations
35B06Symmetries, invariants, etc. (PDE)
35A24Methods of ordinary differential equations for PDE
34A05Methods of solution of ODE
Full Text: DOI
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