Stable nonlinear modes sustained by gauge fields

TL;DR

This paper demonstrates how gauge fields influence the existence, stability, and characteristics of solitons in a two-dimensional nonlinear Schrödinger equation, revealing that curvature can enable stable localized states without external confinement.

Contribution

It uncovers the distinct roles of pure and non-pure gauge components in soliton dynamics and shows that curvature can support stable solitons in repulsive media without external traps.

Findings

Curvature enables stable localized solitons in repulsive media.

Pure gauge affects the stability of soliton modes.

Solutions can be represented as envelopes modulating stationary states.

Abstract

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 \rtext{non-pure gauge} generating \rtext{effective potential}, the roles of these components in soliton dynamics are different: the \btext{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 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.