Solitons, Lumps, breathers and rouge wave solutions to the (3+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt model

Abstract

The mixed localized wave solutions and their interaction have fascinated the vast age of plasma physics, fluid mechanics, and ocean dynamics, thanks to advances in nonlinear shallow water waves theory. In this paper, we conduct an analytical investigation of the (3+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt model. For a deeper understanding of the integrability characteristics of the governing model, the Hirota’s bilinear form has been used to exhibit a variety of wave patterns, such as the Rogue wave solution and interactions between lump wave and periodic wave solutions. Additionally, by using the exp(−ϕ(ξ)) expansion method, certain novel travelling wave shapes are created. In order to understand the dynamics of the governing model, many exciting graphical representations are demonstrated at the conclusion in the form of 3D, 2D, and contour plots. As a result, we created unique bell-shaped solutions, bright soliton solutions, and periodic wave solutions. The discovered results are highly positive and can also be used to assess the characteristics of different complex dynamical models that have emerged in more modern science and engineering.