Multiple Soliton Solutions of Generalized Reaction Duffing Model Arising in Various Mechanical Systems

Abstract

In this paper, we employ some ansatz transformations to investigate various nonlinear waves for a well-known model, the generalized reaction Duffing model, including lump soliton, rogue waves, breather waves, Ma-breather, and Kuznetsov-Ma-breather. The standard Duffing equation is expanded upon in the generalized Duffing model, which adds more terms to take into consideration for more complex behaviors. The generalized reaction Duffing model is useful in many domains, such as electrical engineering, biomechanics, climate research, seismic research, chaos theory, and many more, due to its rich behavior and nonlinear dynamic. Lump soliton is a robust, confined, self-reinforcing wave solution to non linear partial differential equations. Breather waves are periodic, specific solutions in nonlinear wave systems that preserve their amplitude and structure. Rogue waves, which pose a hazard to marine safety, are unexpectedly strong and sharp ocean surface waves that diverge greatly from the surrounding wave pattern. They frequently appear in solitary and apparently random situations. The solutions are graphically displayed using contour, 3D, and 2D graphs.