# Solitons under spatially localized cubic-quintic-septimal nonlinearities

## TL;DR

This paper investigates the stability of solitons in a nonlinear Schrödinger equation with spatially localized cubic, quintic, and septimal nonlinearities, revealing conditions for stable high-power light beams in optical waveguides.

## Contribution

It introduces a model with combined cubic, quintic, and septimal nonlinearities confined in space, providing analytical and numerical stability analysis, and highlights the potential for high-power beam guidance.

## Key findings

- Stability regions align with the Vakhitov-Kolokolov criterion.
- Tight confinement increases maximum stable soliton power with defocusing quintic.
- Analytical solutions are derived for the limit case of delta-function confinement.

## Abstract

We explore stability regions for solitons in the nonlinear Schrodinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign. This setting can be implemented in optical waveguides based on colloids of nanoparticles. The solitons stability is identified by solving linearized equations for small perturbations, and is found to fully comply with the Vakhitov-Kolokolov criterion. In the limit case of tight confinement of the nonlinearity, results are obtained in an analytical form, approximating the confinement profile by a delta-function. It is found that the confinement greatly increases the largest total power of stable solitons, in the case when the quintic term is defocusing, which suggests a possibility to create tightly confined high-power light beams guided by the spatial modulation of the local nonlinearity strength.