We reveal the universal effect of gauge fields on the existence, evolution, and stability of solitons in the spinor multidimensional nonlinear Schrödinger equation. Focusing on the two-dimensional case, we show that when gauge field can be split in a pure gauge and a nonpure gauge generating effective potential, the roles of these components in soliton dynamics are different: the localization characteristics 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 which may depend on the pure gauge implicitly through the effective potential, and 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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标量场保持稳定的非线性模式。

我们揭示了规范场对旋量多维非线性Schrödinger方程中孤子的存在，演化和稳定性的普遍影响。着眼于二维情况，我们表明，当可以在一个纯量规和一个非纯量规中将量规场划分为产生有效电势时，这些分量在孤子动力学中的作用是不同的：新兴态的局域特性由曲率，而纯规范会影响模式的稳定性。可以分别将解决方案精确地表示为包络，该包络可以通过有效电势隐含地依赖于纯量规，并调制与曲率无关的固定载波模式状态。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，