Travelling wave solutions for the (2 + 1) dimensional Nizhnik–Novikov–Veselov equation

Using an auxiliary ordinary differential equation method, we have obtained many exact travelling wave solutions for the (2 + 1) dimensional Nizhnik–Novikov–Veselov equation which is considered as a model for an incompressible fluid. The key of this method is to construct appropriate travelling wave functions in terms of solving a system of nonlinear algebraic equations. The method is also extended to the case of other nonlinear partial differential equations with solitary wave solutions, triangular periodic wave solutions and elliptic function solutions et al.