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Symbolic-computation study on the (2+1)-dimensional dispersive long wave system. (English) Zbl 1385.76007

Summary: Under investigation in this paper is the (2+1)-dimensional dispersive long wave system, which describes the hydrodynamics of wide channels or open seas of finite depth. Its bilinear form is derived with the generalized Bell polynomials. New analytic solutions are obtained via symbolic computation, based on which the propagation of the water waves is analyzed graphically and the different phenomena of fission and fusion are revealed. Additionally, the bilinear auto-Bäcklund transformation is obtained by the generalized Bell polynomials.

MSC:

76B25 Solitary waves for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
68W30 Symbolic computation and algebraic computation
74J20 Wave scattering in solid mechanics
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
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