Abundant exact solutions of a new (2+1)-dimensional extended KadomtsevPetviashvili equation

Various novel exact solutions are constructed of a new (2+1)-dimensional extended Kadomtsev-Petviashvili equation, which differs from the classical KP equation by additional second-order temporal derivative terms and mixed derivative terms. This (2 + 1)-dimensional nonlinear equation can describe more complicated shallow water wave dynamics with higher-oation method and the consistent tanh expansion method, arerder time evolution effects. Three distinct methods, namely the exp(–Φ(ξ)) method, the new auxiliary equ systematically employed to the extended Kadomtsev-Petviashvili equation for the first time, yielding hyperbolic, trigonometric and rational function solutions, as well as resonant soliton, solitonperiodic and soliton-cnoidal interaction solution that enrich the exact solutions of this integrable equation. These results provide significant theoretical insights into the shallow water dynamics behaviors of this integrable model with higher-order time evolution effects. The corresponding two-dimensional plots, three-dimensional plots and density plots of these exact solutions are also given graphically with proper arbitrary constants selection.