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Symbolic computation and construction of soliton-like solutions to the \((2 + 1)\)-dimensional dispersive long-wave equations. (English) Zbl 1211.35234

Summary: By means of a new Riccati equation expansion method, we consider the \((2 + 1)\)-dimensional dispersive long-wave equations \(\eta_{y,t}+\eta_{xx}+1/2u^2_{xy}=0\), \(\eta_t+(u_{\eta}+u+u_{xy})_x=0\). As a result, we not only can successfully recover the previously known formal solutions obtained by known tanh function methods but also construct new and more general formal solutions. The solutions obtained include the nontravelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, triangular functions solutions.

MSC:

35Q51 Soliton equations
35-04 Software, source code, etc. for problems pertaining to partial differential equations
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