Lie symmetry analysis, optimal system and exact solutions for variable-coefficients Boiti-Leon-Manna-Pempinelli equation

In this paper, the constant coefficients are extended to variable coefficients in the Boiti-Leon-MannaPempinelli(BLMP) equation, and its optimal system, exact solutions, conservation laws are studied. First, the infinitesimal generators for independent variables of the variable-coefficient Boiti-LeonManna-Pempinelli(vcBLMP) equation are solved by using the Lie symmetry analysis method. Subsequently, the optimal system of the vcBLMP equation is solved, and then the equations are subjected to similarity reduction, the partial differential equations(PDEs) are gained. Based on these PDEs, the representative equations are converted into ordinary differential equations(ODEs) by traveling wave transformation, and some new exact solutions of vcBLMP equation is obtained by using (G'/ G)-expansion method and tanh-function method, such as the kink solutions, periodic solutions and soliton solutions. According to the obtained solutions, the corresponding images are plotted in order to facilitate the presentation of structural features of the solutions. At the end, the vcBLMP equation is proved to be nonlinear self-adjoint equation and the conservation laws of vcBLMP are solved.