Wave structures and its evolution modeled by variant Mikhailov-Novikov-Wang equation

Abstract In this study, we first transform the variant Mikhailov-Novikov-Wang equation into a corresponding dynamical system using the traveling wave transform. In order to derive the Gaussian soliton solutions of the equation, the generalized trial equation method is employed. We employ the complete discrimination system for polynomial method for qualitative analysis and concluded the existence of periodic and soliton solutions of the equation by exploring the relationship between the roots and coefficients of the polynomials without explicitly solving the solutions. Further quantitative analysis verifies these conclusions by presenting the corresponding solutions. Sensitivity evaluation is conducted via multiple situations using numerical simulations, which demonstrate how the initial conditions influence the evolution of the system. Additionally, chaotic phenomena are also discovered by introducing a perturbation term, confirming the presence of chaotic behavior. To the best of our awareness, this study is the first to explore the sensitivity and chaotic properties of this equation. Considering the significances of the equation in plasma physics and fluid dynamics, that we obtained can have the practical applications in the real-physical world.