Bright solitons from defocusing nonlinearities

TL;DR

This paper demonstrates that in media with spatially increasing defocusing nonlinearity, stable bright solitons can exist in one, two, and three dimensions, including complex vortex states, with potential for robust quasi-particle behavior.

Contribution

It introduces a new class of stable bright solitons supported by inhomogeneous defocusing nonlinearities, including analytical solutions and approximations for various dimensions and states.

Findings

Stable 1D, 2D, and 3D solitons identified.

Existence of vortex solitons with high topological charges.

Solitons exhibit elastic collisions and coherent motion.

Abstract

We report that defocusing cubic media with spatially inhomogeneous nonlinearity, whose strength increases rapidly enough toward the periphery, can support stable bright localized modes. Such nonlinearity landscapes give rise to a variety of stable solitons in all three dimensions, including 1D fundamental and multihump states, 2D vortex solitons with arbitrarily high topological charges, and fundamental solitons in 3D. Solitons maintain their coherence in the state of motion, oscillating in the nonlinear potential as robust quasi-particles and colliding elastically. In addition to numerically found soliton families, particular solutions are found in an exact analytical form, and accurate approximations are developed for the entire families, including moving solitons.