Analysis and Classification of Multi-Soliton Solutions in Coupled Nonlinear Evolution Equations with Time-Dependent Coefficients
Abstract
This research investigates the analytical and numerical aspects of coupled nonlinear evolution
equations (CNLEEs) with time-dependent coefficients, focusing on their multi-soliton solutions.
We employ multiple analytical techniques, including the Hirota bilinear method and Darboux
transformation, to derive exact solutions under various initial and boundary conditions. The
study reveals novel families of solutions, including shape-changing solitons and breather modes,
which exhibit distinct behavioral characteristics under different parametric conditions. Our
analysis demonstrates that time-dependent coefficients significantly influence the interaction
dynamics and stability properties of multi-soliton solutions. We establish a comprehensive
classification framework for these solutions based on their geometric properties and interaction
patterns. The numerical simulations validate our analytical findings and provide insights into
the long-term evolution of these solutions. The results have important implications for
applications in optical fiber communications and Bose-Einstein condensates, where precise
control over soliton interactions is crucial. Furthermore, we identify critical parameter regimes
where stable multi-soliton propagation can be achieved, offering practical guidelines for
experimental implementations.
How to Cite
Anupma, Dr. Jogender, "Analysis and Classification of Multi-Soliton Solutions in Coupled Nonlinear Evolution Equations with Time-Dependent Coefficients", Vol. 3, Issue 2, 28-05-2025, pp. 60-69.
