Beyond travelling waves: A new algorithm for solving nonlinear evolution equations

In physical sciences, nonlinear evolution equations (NLEEs) and their exact solutions are of fundamental importance. However, there is no answer yet as to whether or not one is able to go beyond travelling waves with the recently proposed tanh method. In this paper, without loss of conciseness and straightforwardness, a generalized tanh algorithm with symbolic computation is suggested for the construction of new soliton-typed solutions for certain NLEEs. Illustrative examples are presented for several equations of current interest in the physical sciences, i.e., the (2+1)-dimensional breaking soliton equation, the (3+1)-dimensional generalized shallow water wave equation, and the coupled set of the (2+1)-dimensional integrable dispersive long wave equations.