The lump solutions for the (2+1)-dimensional Nizhnik–Novikov–Veselov equations

The exact solutions for the (2+1)-dimensional Nizhnik–Novikov–Veselov (NNV) equations are investigated via Maple software. According to the Hirota bilinear form of the NNV equations, lump solutions are mainly obtained by the limit method of the heteroclinic test functions with initial values. Furthermore, the interaction solutions of the lump and N-soliton solutions are researched with the aid of new test functions which consist of the quadratic polynomial functions and the exponential functions. Especially, the sufficient conditions for the existence of the interactions solutions for NNV equations are given.