Deterministic and Chaotic Analysis in Multi-Order Solitons and Lump Solutions of a Generalized Nonlinear Evolution Equation via the Duffing Chaotic System

In this manuscript, a (3+1)-dimensional nonlinear evolution equation (EE), which is a generalization of the (3+1)-dimensional Hirota bilinear equation and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation, is explored. The Hirota direct method, along with the Cole-Hopf transformation, is utilized to achieve the bilinearization of the considered equation. Via a suitable auxiliary function (AF) and bilinear form, multiple soliton and lump solutions and their interaction with kink solitons are derived. Moreover, the chaotic behavior of the acquired soliton solutions is demonstrated in the light of the Duffing chaotic system. All the results are portrayed using 3D and density plots to show the behavior of the obtained solutions.