Higher order Soliton Complexes in Coupled Nonlinear Schr\"odinger Equation with Variable Coefficients

TL;DR

This paper derives explicit three-soliton solutions for a variable coefficient coupled nonlinear Schrödinger equation, analyzing their interactions and energy sharing, with implications for optical device development.

Contribution

It provides the first explicit three-soliton solutions and detailed interaction analysis for variable coefficient coupled NLS equations, revealing new energy sharing phenomena.

Findings

Energy sharing occurs without direct collision.

Interaction patterns depend on soliton parameters.

Bound states exhibit unique asymptotic features.

Abstract

We present the explicit dark-bright three soliton solution and the associated spectral problem for the variable coefficient integrable coupled NLS equation. Using asymptotic analysis as well as graphical analysis we study the interactions in soliton complexes. We present a correlation between the soliton parameters and the interaction pattern in three soliton complexes. Using asymptotic analysis, we present a few interesting features of complex three soliton bound state and interaction of dark-bright two soliton complex with a regular soliton. Using three soliton interactions we have shown that the energy sharing take place between soliton even when the soliton do not collide with each other. The results found by us might be useful for the development of soliton control, all optical gates as well as all optical switching devices. We hope that the analysis of three soliton complexes would be useful for a better understanding of soliton interactions in nonlinear fiber as well as in a bulk medium.