Optical solitons, qualitative analysis and multistability response to study the dynamical behaviour of light wave promulgation

Abstract

Our aim is to explore novel optical solitons within the context of an extended higher-order nonlinear Schrödinger equation that governs the behaviour of propagating light waves. Primarily, this research finds abundant types of solitons, such as singular, kink and trigonometric functions subject to certain constraint conditions. We have utilized [Formula: see text]-expansion method, which has proved effective in retrieving these solitons and presenting them for further analysis. The model's dynamic behaviour is then investigated through bifurcation, quasi-periodic oscillations, chaotic behaviour, and sensitivity. These include methods like phase portrait rendering, time series scrutiny, Lyapunov exponents calculation, and the assessment of multi-stability. Finally, sensitivity analysis is conducted at three distinct initial conditions, revealing that the model displays a high level of sensitivity, with substantial alterations occurring in response to minor changes in the initial conditions. The results of this study are revolutionary, intriguing, and possess crucial theoretical importance in evolution disruptions.

Keywords

• Generalized higher-order NLSE
• -expansion method
• chaotic behaviour
• bifurcation analysis
• sensitivity analysis