We reveal the universal effect of gauge fields on the existence, evolution, and stability of solitons in the spinor multidimensional nonlinear Schr"{o}dinger equation. Focusing on the two-dimensional case, we show that when gauge field can be split in a pure gauge and a generating , the roles of these components in soliton dynamics are different: the of emerging states are determined by the curvature, while pure gauge affects the stability of the modes. Respectively the solutions can be exactly represented as the envelopes independent of the pure gauge, modulating stationary carrier-mode states, which are independent of the curvature. Our central finding is that nonzero curvature can lead to the existence of unusual modes, in particular, enabling stable localized self-trapped fundamental and vortex-carrying states in media with constant repulsive interactions without additional external confining potentials and even in the expulsive external traps.

中文翻译：

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规范场维持的稳定非线性模式

我们揭示了规范场对自旋多维非线性Schr“ {o} dinger方程中孤子的存在，演化和稳定性的普遍影响。针对二维情况，我们证明了当规范场可以分解为一个纯规范和生成，这些分量在孤子动力学中的作用是不同的：新兴状态的状态由曲率决定，而纯规范影响模态的稳定性，分别可以将解精确地表示为与包络无关的包络。纯规范的，调制的，稳定的载流子态，与曲率无关。我们的主要发现是，非零曲率会导致异常模式的存在，特别是，能够在具有不断排斥作用的介质中实现稳定的局部自陷基本和涡旋状态，而不会产生额外的外部约束电位，甚至在排斥性外部陷阱中也是如此。