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Generalized transformations and abundant new families of exact solutions for (2 + 1)-dimensional dispersive long wave equations. (English) Zbl 1064.35030

The author derives many types of exact solutions of the (2+1)-dimensional dispersive long wave equation by a generalized transformation. In addition the author also obtains many corresponding solitary and periodic wave solutions for the variant Boussinesq equation, as a spherical case of the (2+1)-dimensional dispersive long wave equation. The author shows that, with the aid of symbolic computation and the Wu elimination method, solving nonlinear partial differential equations can be carried out on a computer.

MSC:

35C05 Solutions to PDEs in closed form
35G20 Nonlinear higher-order PDEs
35B10 Periodic solutions to PDEs
35Q51 Soliton equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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References:

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