Novel Soliton Structures and Dynamical Behaviors of Some Physical Models

Abstract

This thesis explores the dynamic behavior and soliton solutions of various nonlinear models with significant applications in nonlinear optics, hydrodynamics, and plasma physics. The study investigates the Lakshamanan-Porsezian-Daniel (LPD) model, addressing the internet bottleneck issue through the incorporation of spatio-temporal dispersion. Utilizing tools such as phase portraits, bifurcation diagrams, Lyapunov exponents, and time series analysis, the generation of quasi-periodic and chaotic patterns is examined. A detailed bifurcation analysis of the generalized Pochhammer-Chree (PC) equation is conducted, revealing complex dynamics and sensitivity to initial conditions. Further, the coupled Higgs field equations are analyzed to obtain periodic and shock-wave profiles using the Jacobi elliptic function (JEF) technique. The dynamical behavior, including quasi-periodic motion and chaotic patterns, is thoroughly investigated. The coupled Benjamin-Bona-Mahony-Korteweg-de Vries (BBM-KdV) system is studied for its soliton solutions and dynamic features, with a focus on chaos detection and the construction of solitary wave structures. Lastly, the complex coupled Maccari system is examined, establishing dark and bright-wave profiles through the Modified Jacobi elliptic function (MJEF) technique. The model’s dynamic characteristics are explored from multiple perspectives, emphasizing phase portrait analysis and sensitivity analysis. This comprehensive investigation enhances the understanding of nonlinear wave propagation and offers insights into predictive modeling and control strategies in nonlinear dynamical systems.