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.

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• Bose-Einstein condensates
• Cold atoms & matter waves
• Optical solitons
• Solitons
• Spinor Bose-Einstein condensates
• Nonlinear waves