Dynamical analysis of (4 + 1)-dimensional Davey Srewartson Kadomtsev Petviashvili equation by employing Lie symmetry approach

Abstract

In this study, (4+1)-dimensional Davey Srewartson Kadomtsev Petviashvili equation is investigated, which can be employed to depict internal wave interactions encompassing both elastic and non-elastic behaviors. Initially, the translational symmetries of the equation are identified by employing Lie symmetry method. Then, by utilizing these symmetries, the discussed model is translated into an ordinary differential equation. The new auxiliary equation approach is then employed to obtain precise solutions, and the results are visually represented. Afterward, the dynamical behavior of the equation is analyzed from multiple perspectives, including bifurcation, chaos, and sensitivity analysis. Bifurcation is conducted at fixed points, while an external force is applied to the dynamical system, leading to the discovery of chaotic behavior using various tools such as 3D and 2D phase plots, time series plots, Poincaré maps, and multistability analysis. Furthermore, sensitive nature of the model is examined at different initial values, revealing the significant sensitivity of the proposed model, where even small changes in the initial conditions result in notable variations. At the end, conclusion is presented.