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A new (2+1)-dimensional soliton equation and its spectral problems are presented. The Darboux transformation with multi-parameters for the spectral problems is constructed with the help of a gauge transformation. And by using the Darboux transformation, some new bidirectional soliton solutions of the (2+1)-dimensional soliton equation are obtained. An interesting solution of three-peak soliton has...
By using the general solutions of a coupled Riccati equations and the relations between them a direct algebra method is described to construct several kinds of closed-form travelling wave solutions for some nonlinear differential equations. By this method three important nonlinear partial differential equations are studied and, in addition to rederiving all known solutions, several new solutions are...
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