Exploring Soliton Solutions in Nonlinear Schrödinger Equations- A Comprehensive Analysis (International Journal of Food and Nutritional Sciences, 2022)
This study provides a comprehensive analysis of soliton solutions in the Nonlinear Schrödinger Equation (NLSE). Utilizing a combination of analytical and numerical methods, the research investigates the properties and dynamics of solitons in one-dimensional and multi-dimensional settings. Key findings include the confirmation of soliton stability and shape preservation in one-dimensional systems, vital for applications such as optical fiber communications. In multi-dimensional contexts, the study reveals the formation and stability of complex soliton structures, including ring-shaped solitons, showcasing the intricate behavior of solitons in higher-dimensional spaces. The investigation into soliton collisions provides insights into various interaction outcomes, including elastic collisions, fusion, and fission processes. These results not only validate existing theoretical predictions but also offer new perspectives on soliton behavior in nonlinear media. The study, while robust, acknowledges limitations in computational modeling and the idealized nature of some scenarios. Future work is suggested in developing more sophisticated models, exploring additional influencing factors, and investigating practical applications in technology and science.