Bifurcation, chaotic and multistability analysis of the $(2+1)$-dimensional elliptic nonlinear Schrödinger equation with external perturbation

Abstract

This paper presents a theory of weakly nonlinear wave propagation in superposed fluids in the existence of magnetic fields. The extended direct algebraic approach has been utilized to draw and examine the solitonic wave solutions to the -dimensional elliptic nonlinear Schrödinger equation (ENLSE). These obtained solutions are more novel and valuable to researchers for understanding physical marvels. The graphical representation of some selected exact solutions is reported with different parametric values to show their propagation. Furthermore, the examined equation is changed into the planer dynamical structure by utilizing Galilean transformation. By utilizing the idea of bifurcation, all the possible phase portraits of nonlinear and super nonlinear traveling wave solutions have been explored. Moreover, after adding an external force to the dynamical system, the periodic, quasi-periodic, and chaotic behaviors of the 2D, 3D and time series are also observed. Meantime, for various initial conditions, the sensitivity of the derived solutions is investigated in detail. It is discovered that the considered equation is multistable for the same values of parameters but different initial conditions.