Generalized algebraic method and new exact traveling wave solutions for (2 + 1)-dimensional dispersive long wave equation

With the help of the symbolic computation system Maple, a new generalized algebraic method to uniformly construct solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz. As an application of the method, we choose a (2 + 1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by the method proposed by Fan [E.G. Fan, Phys. Lett. A 300 (2002) 243] and find other new and more general solutions at the same time, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solutions, hyperbolic, and soliton solutions, Jacobi, and Weierstrass doubly periodic wave solutions.