Study of complex dynamics and novel soliton solutions of the Kraenkel-Manna-Merle model describing saturated ferromagnetic materials

Abstract

This paper introduces a framework for nonlinear short wave propagation in an external field for saturated ferromagnetic materials with zero conductivity: the Kraenkel-Manna-Merle system. New solutions are produced via the G′/(bG′+G+a)-expansion technique. The suggested method is easier to understand, more precise, and simpler to compute. Specifically, a set of singular-periodic and kink-shaped exact soliton solutions is produced. Contour plots, 3D, and 2D visualizations with suitable parametric values are employed to present the computed solutions, which are derived through constraint conditions. For the development of certain novel soliton structures, the arbitrary functions in the solutions are selected. Moreover, bifurcation and chaos theory are applied to the primary dynamical system in order to provide a qualitative analysis of the system under study. Phase portraits of bifurcation are presented at fixed locations to illustrate different situations about parameter values in the dynamic system. However, adopting techniques for identifying chaos in a dynamical system and applying an external force verifies the occurrence of chaotic behavior in system. These results offer new perspectives that can enhance understanding of the dynamics of the KMM system.

Keywords

• G′/(bG′+G+a)-expansion method
• Soliton solutions
• Dynamical system
• Bifurcation
• Chaos analysis