Exact solutions and conservation laws of a new fourth-order nonlinear (3+1)-dimensional KadomtsevPetviashvili-like equation

Abstract

In this paper, we investigate an inclusive innovative fourth-order nonlinear Kadomtsev-Petviashvili-like model, a three dimensional nonlinear partial differential equation. The focus is on utilizing the Lie symmetry method to derive exact solutions that demonstrate significant advancements in the model. Initially, a systematic approach is employed to compute the Lie point symmetries of the equation. These symmetries play a crucial role in identifying a diverse range of group invariant results for the model. The obtained solutions encompass logarithmic, exponential, and hyperbolic functions, as well as elliptic integral functions, with the latter being the most general solutions. Additionally, several noteworthy algebraic function solutions are also discovered. This research distinguishes itself by presenting a wealth of results that exhibit substantial variation. Furthermore, the dynamics of the solutions are thoroughly explored through diagrammatic analysis using computer software. Towards the conclusion, Ibragimov's theorem is applied to construct various conservation laws for the underlying model. This technique yields a multitude of conservation laws, which are subsequently discussed and highlighted.