Symbolic Computation of Lump Solutions to a Combined Equation Involving Three Types of Nonlinear Terms

Abstract

This paper aims to compute lump solutions to a combined fourth-order equation involving three types of nonlinear terms in (2+1)-dimensions via symbolic computations. The combined nonlinear equation contains all second-order linear terms and it possesses a Hirota bilinear form under two logarithmic transformations. Two classes of explicit lump solutions are determined, which are associated with two cases of the coefficients in the model equation. Two illustrative examples of the combined nonlinear equation are presented, along with lump solutions and their representative three-dimensional plots, contour plots and density plots.