Solitary wave solutions of GKP equation with (2+1)dimensional variable-coefficients in dynamic systems

At present, the solution and qualitative analysis of nonlinear partial differential equations occupy a very important position in the study of dynamics. In this paper, the bilinear Bäcklund transformation of the (2+1)-dimensional variable-coefficient $Gardner-KP\left(GKP\right)$ equation is deduced by virtue of Hirota bilinear form, which consists of seven bilinear equations and involves ten arbitrary parameters. On the basis of the bilinear Bäcklund transformation, the traveling wave solution of the equation is obtained. Then the test function of the interaction solution of the positive quadratic function and exponential function of the (2+1)-dimensional variable-coefficient $GKP$ equation is constructed, and then the test function of the positive quadratic function, hyperbolic cosine function and the interaction solution of the cosine function is constructed. With the help of mathematical symbol software Maple and Mathematica, the solitary wave solutions of (2+1)-dimensional variable-coefficient $GKP$ equation is obtained by using Maple and Mathematica, and the interaction phenomena between a Lump wave and a Kink wave, a Lump wave and Multi-Kink waves are discussed.