Analytical study on two new (3 + 1)-dimensional Painlevé integrable equations: Kink, lump, and multiple soliton solutions in fluid mediums

Abstract

In this work, two new (3 + 1)-dimensional integrable wave equations are investigated. The complete Painlevé integrability of the two suggested equations will be investigated using Mathematica. We employ the method of Hirota to formally derive two sets of multiple soliton solutions for the two suggested models. Additionally, using symbolic computation with Maple, we provide a variety of lump solutions for the two suggested models. Other exact solutions of distinct structures, such as periodic, singular, and many other physical nonlinear structures, will be determined. We should mention here that the proposed two new models will assist many authors that are working in the field of fluids and plasma physics, in understanding the scenarios of the nonlinear waves that arise in different physical systems. Also, this study will contribute to understanding the nature of nonlinear waves that arise in the seas and oceans.