A new general algebraic method with symbolic computation to construct new travelling wave solution for the (1 + 1)-dimensional dispersive long wave equation

With the aid of symbolic computation, a new algebraic method, named Riccati equation rational expansion (RERE) method, is devised for constructing multiple travelling wave solutions for nonlinear evolution equations (NEEs). Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recover the results by most known algebraic methods, but also provides new and more general solutions. With the aid of symbolic computation, we choose (1 + 1)-dimensional dispersive long wave equation (DLWE) to illustrate our method. As a result, we obtain many types of solutions including rational form solitary wave solutions, triangular periodic wave solutions and rational wave solutions. The properties of the new solitary wave solutions are shown by some figures.