Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity

TL;DR

This paper shows that radially inhomogeneous self-focusing nonlinearity in 2D can stabilize fundamental solitons against collapse, using analytical and numerical methods, and extends the concept to 1D quintic nonlinearity stabilization.

Contribution

It introduces a novel stabilization mechanism for 2D solitons via radially inhomogeneous nonlinearity, supported by analytical and numerical evidence.

Findings

Radial inhomogeneity stabilizes 2D solitons against collapse.

Stability interval scales linearly with contrast for small contrast.

Exact stabilization demonstrated for 1D quintic solitons.

Abstract

We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the two-dimensional (2D) geometry, in the form of a circle with contrast $\Delta g$ of the SF coefficient relative to the ambient medium with a weaker nonlinearity, stabilizes a family of fundamental solitons against the critical collapse. The result is obtained in an analytical form, using the variational approximation (VA) and Vakhitov-Kolokolov (VK) stability criterion, and corroborated by numerical computations. For the small contrast, the stability interval of the soliton's norm scales as $\Delta N\sim \Delta g$ (the replacement of the circle by an annulus leads to a reduction of the stability region by perturbations breaking the axial symmetry). To further illustrate this mechanism, we demonstrate, in an exact form, the stabilization of 1D solitons against the critical collapse under the action of a locally enhanced quintic SF nonlinearity.