Nonautonomous Motion Study on Accelerated and Decelerated Lump Waves for a (3 + 1)-Dimensional Generalized Shallow Water Wave Equation with Variable Coefficients

Abstract

Under investigation in this paper is a (3 + 1)-dimensional variable-coefficient generalized shallow water wave equation. The exact lump solutions of this equation are presented by virtue of its bilinear form and symbolic computation. Compared with the solutions of the previous cases, these solutions contain two inhomogeneous coefficients, which can show some interesting nonautonomous characteristics. Three types of dispersion coefficients are considered, including the periodic, exponential, and linear modulations. The corresponding nonautonomous lump waves have different characteristics of trajectories and velocities. The periodic fission and fusion interaction between a lump wave and a kink soliton is discussed graphically.