Sun, Kun; Tian, Bo; Liu, Wen-Jun; Li, Min; Qu, Qi-Xing; Jiang, Yan Symbolic-computation study on the (2+1)-dimensional dispersive long wave system. (English) Zbl 1385.76007 SIAM J. Appl. Math. 70, No. 7, 2259-2272 (2010). 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. Cited in 6 Documents 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 Keywords:(2+1)-dimensional dispersive long wave system; generalized Bell polynomials; bilinear form; bilinear auto-Bäcklund transformation; symbolic computation PDFBibTeX XMLCite \textit{K. Sun} et al., SIAM J. Appl. Math. 70, No. 7, 2259--2272 (2010; Zbl 1385.76007) Full Text: DOI