Lump solutions of a nonlinear PDE containing a third-order derivative of time

Abstract

A nonlinear partial differential equation combining with a third-order derivative of the time variable DxDt3 is studied. By adding a new fourth-order derivative term, its lump solutions are explicitly constructed by the Hirota bilinear method and symbolic computation. Furthermore, the effect of the new fourth-order derivative term on the solution is discussed. The dynamical behaviors of two particular lump solutions are analyzed with different choices of the parameters.