The influence of initial solutions to exact solutions of the (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equations

The (2+1)-dimensional generalized Nizhnik-Novikov-Veselov equations (GNNVEs) are investigated in order to search the influence of initial solution to exact solutions. The GNNVEs are converted into the combined equations of differently two bilinear forms by means of the homogeneous balance of undetermined coefficients method. Accordingly, the two class of exact N-soliton solutions and three wave solutions are obtained respectively by using the Hirota direct method combined with the simplified version of Hereman and the three wave method. The proposed method is also a standard and computable method, which can be generalized to deal with some nonlinear partial differential equations (NLPDEs).