Interaction between kink solitary wave and rogue wave, new periodic cross-kink wave solutions and other exact solutions to the (4 + 1)-dimensional BLMP model

Abstract

In this study, some new solutions to the (4+1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) model representing the wave propagation through incompressible fluids. In shallow water, the linearization of the wave structure needs more critical wave capacity conditions than in deep water, and the strong nonlinear features are visible. The obtained solutions may be applied in the demonstration of this model in some better way. These solutions are in the form of interaction between kink solitary wave and rogue wave, new periodic cross-kink wave solutions and other exact solutions with certain conditions. The achieved solutions are also verified by using the latest computational software such as MATHEMATICA. The modified integration techniques, the Hirota bilinear method and the extended (G′/G)-expansion method are utilized to secure the solutions. The obtained solutions are also explained by 3D, 2D and contour graphs. These results may helpful for the further study of the model in future.