Multistability and dynamic behavior of non-linear wave solutions for analytical kink periodic and quasi-periodic wave structures in plasma physics

Abstract

Multistability and dynamic behavior of non-linear wave solutions of unperturbed and perturbed with FitzHugh–Nagumo (FHN) equation is measured using analytical and numerical methods. For unperturbed model a variety of solitonic structures are calculated using a direct algebraic method. Thereafter, the examine model is transformed into a dynamic system with the help of the Galilean transformation and a bifurcation behavior is reported. To choose various particular values of the parameters, we determine single soliton, kinky periodic, bell type waves. In particular, we find both kink waves and the bright and dark bell type from solutions and interactions between waves at different times and solitons. In this work, the dynamics of the low-level model, which controls the interaction between the operator associated with a non-linear wave solution and the multi-stability due to periodic and quasi-periodic deviations, are investigated. Different kinds of cyclic firing diagram emanate abruptly saddle node bifurcations. The parameter territory in which different periodic solutions is also found. In addition, sensitivity analysis is used for a variety of initial values to analyze periodic and quasi-periodic behavior.

Keywords

• Soliton solutions
• Regularized long wave equation
• Non-linear wave solutions
• Bifurcation behavior