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

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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.