Soliton, breather, lump, interaction solutions and chaotic behavior for the (2+1)-dimensional KPSKR equation

Abstract

Nonlinear evolution equations are widely applied in various fields, and understanding their solutions is crucial for predicting and controlling the behavior of complex systems. In this paper, the (2+1)-dimensional Kadomtsev–Petviashvili–Sawada–Kotera–Ramani (KPSKR) equation is investigated, which has rich physical significance in nonlinear waves. Making use of Hirota’s bilinear form, soliton, breather and lump solutions of the (2+1)-dimensional KPSKR equation are derived. The interactions between lump solutions and exponential function, as well as between lump solutions and hyperbolic cosine function, are explored. Furthermore, the chaotic behavior of 1-soliton, 2-soliton, lump and interaction solutions are studied via applying the Duffing chaotic system. The physical structure and characteristics of begotten results are illustrated through 3D plots and corresponding two-dimensional profiles. These results indicate that the strategies utilized are more direct and effective, enriching the study of dynamics in high-dimensional nonlinear differential equations.