# A purely Kerr nonlinear model admitting flat-top solitons

## TL;DR

This paper introduces a new Kerr nonlinear model with spatially modulated self-repulsive nonlinearity that supports stable flat-top solitons, including fundamental, multipole, and vortex types, without requiring competing nonlinearities.

## Contribution

The study presents a purely Kerr nonlinear model capable of supporting flat-top solitons, providing exact solutions and stability analysis, expanding the understanding of soliton formation in nonlinear media.

## Key findings

- Exact analytical solutions for stable flat-top solitons in 1D.
- Stable flat-top solitons include fundamental, multipole, and vortex types.
- Identification of stability and instability regions for various soliton configurations.

## Abstract

We elaborate one- and two-dimensional (1D and 2D) models of media with self-repulsive cubic nonlinearity, whose local strength is subject to spatial modulation that admits the existence of flat-top solitons of various types, including fundamental ones, 1D multipoles, and 2D vortices. Previously, solitons of this type were only produced by models with competing nonlinearities. The present setting may be implemented in optics and Bose-Einstein condensates. The 1D version gives rise to an exact analytical solution for stable flat-top solitons, and generic families may be predicted by means of the Thomas-Fermi approximation. Stability of the obtained flat-top solitons is analyzed by means of linear-stability analysis and direct simulations. Fundamental solitons and 1D multipoles with $k=1$ and $2$ nodes, as well as vortices with winding number $m=1$, are completely stable. For multipoles with $k\geq 3$ and vortices with $m\geq 2$, alternating stripes of stability and instability are identified in their parameter spaces.