Stability and dynamical analysis of the Davey-Stewartson model

Abstract

This study investigates the nonlinear coupled Davey-Stewartson Fokas system, a mathematical model describing pulse propagation in monomode optical fibers. Employing a powerful analytical technique, we derive novel periodic and solitary wave solutions, including bright, dark, periodic and kink soliton. These solutions significantly advance our understanding of the precise dynamics of solitons in nonlinear optics. The proposed methods effectively discover and characterize new solitary wave solutions, providing deeper insights into the model's behavior. These computational techniques hold enormous promise for various scientific applications and enhance our knowledge of fundamental dynamics. This paper visually represents soliton solutions in the form of 2D, 3D, and contour plots. By applying the Galilean transformation and using appropriate parameter values, we obtain the planar dynamical system, which aids in the dynamical analysis of the Davey-Stewartson Fokas system. Using the planer dynamical system to examine the phase-portrait analysis of the system. Also examine the sensitivity analysis of the system's reaction to various initial conditions during both the initial and intransitive phases. Furthermore, we investigate the chaotic behavior by adding an external force, examining whether the planar dynamical system exhibits periodic, quasi-periodic and chaotic patterns.