New nonlinear systems admitting Virasoro-type symmetry algebra and group-invariant solutions. (English) Zbl 1474.35045

Summary: With the aid of symbolic computation by Maple, we extend the application of Virasoro-type symmetry prolongation method to coupled systems with two-component nonlinear equations. New nonlinear systems admitting infinitely dimensional centerless Virasoro-type symmetry algebra are constructed. Taking one of them as an example, we present some group-invariant solutions to one of the new model systems.


35A30 Geometric theory, characteristics, transformations in context of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)


Full Text: DOI


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