Dark-bright solitons in coupled nonlinear Schr\"odinger equations with unequal dispersion coefficients

TL;DR

This paper investigates dark-bright solitons in a coupled nonlinear Schrödinger system with unequal dispersion, identifying bifurcation points, stability regimes, and the effects of potential traps through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of dark-bright solitons with unequal dispersion coefficients, including bifurcation points, stability regimes, and the impact of trapping potentials.

Findings

Bifurcation points for bright solitons identified.

Potential stability regimes for dark-bright solitons found.

Instability outcomes analyzed via numerical simulations.

Abstract

We study a two-component nonlinear Schr{\"{o}}dinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright-solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes of potential stability, not only of the single-peak ground state (the dark-bright soliton), but also of excited states with one or more zero crossings in the bright component. When the states are identified as unstable, direct numerical simulations are used to investigate the outcome of the instability development. Although our principal focus is on the homogeneous setting, we also briefly touch upon the counterintuitive impact of the potential presence of a parabolic trap on the states of interest.