Applications of the generalized nonlinear evolution equation with symbolic computation approach

Abstract

In this work, we will try to find lump solutions, interaction between lump wave and solitary wave solutions, kink-solitary wave solutions and shock wave-type solutions to (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves. The lump solutions, the interaction between lump wave and solitary wave solutions and kink-solitary wave solutions are derived with symbolic computation based on a logarithmic derivative transform which is derived by the help of Hirota's simple method. The shallow water waves in this equation are associated with some natural problems such as tides, storms, atmospheric currents and tsunamis. For the physical presentation of the solutions, we draw 3D and counter graphics by giving the suitable values to include the free parameters. We believe that disciplines such as mathematical physics, nonlinear dynamics, fluid mechanics and engineering sciences can benefit from this study.