Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients

Abstract

We consider a two-component, two-dimensional nonlinear Schrödinger 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.

14 pages, 10 figures

References in corpus (10)

• Oscillations and interactions of dark and dark-bright solitons in Bose-Einstein condensates
• Double species condensate with tunable interspecies interactions
• Generation of dark-bright soliton trains in superfluid-superfluid counterflow
• The creation of two-dimensional composite solitons in spin-orbit-coupled self-attractive Bose-Einstein condensates in free space
• Interaction of half-quantized vortices in two-component Bose-Einstein condensates
• Dark-bright solitons in coupled nonlinear Schrödinger equations with unequal dispersion coefficients
• $SO(2)$-induced breathing patterns in multi-component Bose-Einstein condensates
• Beating dark-dark solitons and Zitterbewegung in spin-orbit coupled Bose-Einstein condensates
• Domain walls and bubble-droplets in immiscible binary Bose gases
• Interfaces between Bose-Einstein and Tonks-Girardeau atomic gases

Cited by in corpus (7)

• Vortices with massive cores in a binary mixture of Bose-Einstein condensates
• Structured hetero-symmetric quantum droplets
• Relative dynamics of quantum vortices and massive cores in binary BECs
• Controlled engineering of a vortex-bright soliton dynamics using a constant driving force
• Internal Oscillations of a Dark-Bright Soliton in a Harmonic Potential
• Systematic solitary waves from their linear limits in two-component Bose-Einstein condensates with unequal dispersion coefficients
• (In)stability of symbiotic vortex-bright soliton in holographic immiscible binary superfluids