Vortex-soliton complexes in coupled nonlinear Schr\"odinger equations with unequal dispersion coefficients

TL;DR

This paper investigates vortex-soliton complexes in a two-component nonlinear Schrödinger system with unequal dispersion, revealing the existence, stability, and dynamics of multi-ring states and their transformation into stable fundamental solitons.

Contribution

It introduces the concept of vortex-induced potential wells supporting multi-ring and excited radial states in coupled nonlinear Schrödinger equations with unequal dispersion.

Findings

Multi-ring excited states exist for certain dispersion ranges.

Weak instability leads to transformation into fundamental solitons.

Stability can be enhanced by trapping potentials and nonlinear strength adjustments.

Abstract

We consider a two-component, two-dimensional nonlinear Schr\"{o}dinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multi-ring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multi-ring complexes into stable VB solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.