The three-wave method for the asymmetric Nizhnik-Novikov-Vesselov equation

In this paper, the asymmetric Nizhnik-Novikov-Vesselov equation is studied by using extended three-soliton method. The new exact solutions including discontinuous periodic wave solution, two-soliton wave solution, three solitary wave solution and smooth solitary wave solution for the asymmetric Nizhnik-Novikov-Vesselov equation are obtained. Their dynamic properties of some exact solutions are discussed and their profiles of these solutions are given by Maple.