Lie symmetry analysis, bifurcations and exact solutions for the (2+1)-dimensional dissipative long wave system

By the combination of Lie symmetry analysis and dynamical system method, the (2+1)-dimensional dissipative long wave system is studied. First, we get Lie algebra and Lie symmetry group of the system. Then, by using the dynamical system method, the bifurcation and phase portraits of the corresponding traveling system of the system are obtained, it is shown that for different parametric space, the system has infinitely many solitary wave solutions, periodic wave solutions, kink or anti kink wave solutions. At last, the conservation laws of the system are given.