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.

SO(2)-induced breathing patterns in multicomponent Bose-Einstein condensates

“…Figures 3, 4, and 5 depict examples of initially rotated, in order to produce the vortexvortex (VV) state, and dynamically evolved vortex-bright As has been illustrated in the recent study of [38] (even in the absence of a trap) and also in earlier works in the presence of a trap [27], the vortex-bright state is generally stable. As mentioned in Sec.…”

“…We refer the interested reader to Refs. [37][38][39] for a detailed description of the numerical methods employed in this present work. In our numerical computations presented below, we consider values of the trap strength of 0.1,0.2, and 1 in the 1D, 2D, and 3D cases, respectively.…”

Systematic solitary waves from their linear limits in two-component Bose-Einstein condensates with unequal dispersion coefficients

“…Here, the anti-dark soliton is a "bright" soliton sitting on top of a finite rather than zero background. In addition, there are also states where the trapped "bright" component is excited showing one or even multiple phase windings, which we refer to as dark-multi-dark states herein [24,25]. * Electronic address: wenlongcmp@scu.edu.cn Many techniques have been developed for finding solitary wave solutions, see [26] for a brief discussion of some established analytic methods and numerical methods, e.g., the Darboux transformation [27] and the deflation method [28], respectively.…”

Vortices with massive cores in a binary mixture of Bose-Einstein condensates

“…The same symbiotic relationship was shown to constitute the mechanism underlying the robustness of vortexbright soliton complexes [38], the topological extension of the dark-bright soliton configuration to the case where a component hosts one or more vortices. The aforementioned study paved the way to a series of further investigations which highlighted, among various aspects, the spontaneous generation of vortex-bright soliton structures [39], the possibility, for the effective potential well corresponding to the vortex core, to support not only bound states [40], but also multi-ring excited radial state complexes [41], and a rich dynamical scenario for the bright-solitary component [42].…”