Dynamics of lump solutions to the variable coefficients (2+1)-dimensional Burger's and Chaffee-infante equations

Abstract

In many physical situations, variable-coefficient nonlinear partial differential equations provide us with more realistic aspects of media inhomogeneities and boundary nonuniformities than constant-coefficient. In this research, we extract some new structures of lump solutions to some important nonlinear equations with variable coefficients. The equations under consideration are the (2+1)-dimensional Burger's equation (BE) and the (2+1)-dimensional Chaffee-infante equation (CIE). The Hirota bilinear form (HBF) is the basic idea behind the novel lump solutions. By utilizing the HBF, various kind of lump solutions are derived. Additionally, numerical results are presented through the three-dimensional and contour outlooks to observe the advantages of the variable coefficients.