Modeling of the Origin and Interactions of Multisoliton Solutions of the (2+4)KdV Equation

Abstract

Most of the relevant research work has addressed the properties of internal solitons in a greatly simplified environment, usually in the framework of different versions of the two layer fluid. The simplest equation of this class is the well-known Korteweg-de Vries (kdV) equation that describes the motion of weakly nonlinear internal waves in the long-wave limit. However, in many areas of the world’s ocean, the vertical stratification has a clearly pronounced three-layer structure, with well-defined seasonal thermocline at a depth of about 100m or higher. Hence , the need for a redefinition of the famous KdV equation to tackle such scenarios and clearly accounts for nonlinearity in such environments. In this work, we first derived an analytical solution for the (2+4) KdV-like equation which mimics such situations and numerically solved it using the pseudospectral methods due to its robustness. After numerical simulations, we observed that the multisoliton solution interactions, particularly the three soliton solution interaction showed similar properties with the two soliton solution interaction.