Symmetry Reductions And Exact Solutions Of (2+1)-dimensional Boiti-Leon-Manna-Pempinelli Equation

There are many methods to get the solutions of nonlinear partial differentialequations, such as inverse scattering method, prolongation method, B cklundtransformation method, Darboux transformation method, Lie transformation groupmethod, etc. Due to the complexity of nonlinear partial differential equations,exploring the solutions of every equation has certain skills, so far, there is no unifiedmethod. With the development of all kinds methods, not only do people obtain somenew solutions of many nonlinear partial differential equations, but also find the newsolutions have great significance.In this paper, we mainly discuss a kind of solution method and symmetryreduction of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation.First we discuss Lie transformation group of (2+1)-dimensional BLMP equation.The key step is how to solve the infinitesimal element of (2+1)-dimensional BLMPequation.By using the modified CK direct method, we find a large amount of symmetryreductions, and obtain the new exact solutions of (2+1)-dimensional BLMP equation.The method does not use any group theory.In this paper, we mainly use the modified CK direct method and Maple software.