Superfluid vortex multipoles and soliton stripes on a torus
Superfluid vortex multipoles and soliton stripes on a torus
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DOI：
10.1103/physreva.105.063325
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发表时间：
2022-01
影响因子：
2.9
通讯作者：
J. D’Ambroise;R. Carretero-Gonz'alez;P. Schmelcher;P. Kevrekidis
中科院分区：
文献类型：
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作者：
J. D’Ambroise;R. Carretero-Gonz'alez;P. Schmelcher;P. Kevrekidis
研究了环面上非线性薛定谔(NLS)方程涡旋偶极子和四极子组态的存在性、稳定性和动力学。为此，除了环面上的全二维NLS外，我们还使用最近派生的[Phys.A101,053606(2021年)]简化的点涡粒子模型，它被证明与完整的NLS演化非常一致。水平、垂直和对角固定的涡偶极子被识别出来，并沿着环面长宽比和溶液的化学势继续。确定了这些解决方案的稳定窗口。我们还研究了定常涡旋四极构型。在剔除由不变性和对称性引起的相似解后，我们发现总共有16种不同的组态，从水平和垂直排列的四极，到矩形和菱形的四极，再到梯形和不规则的四极。最不稳定和潜在稳定的四极解的稳定性在NLS和简化模型水平上都得到了监测。在环面长宽比的小窗口上，两个四极构型是稳定的，而对于较大的参数窗口，少数四极构型是非常弱的不稳定的。最后，我们通过一系列具有稳态涡旋构型的分叉级联，简要地研究了暗孤子条纹及其联系。
We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schr\"odinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS on the torus, a recently derived [Phys. Rev. A 101, 053606 (2021)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and continued along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontal and vertical aligned quadrupoles, to rectangular and rhomboidal quadrupoles, to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrapole solutions is monitored both at the NLS and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark soliton stripes and their connection, through a series of bifurcation cascades, with steady state vortex configurations.