# Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices

## TL;DR

This paper demonstrates that combining a nonlinear lattice with saturation of quintic nonlinearity can suppress critical collapse in one-dimensional solitons, supporting multiple soliton types with stability confirmed by numerical simulations.

## Contribution

It introduces a novel approach to stabilize 1D solitons against collapse by integrating nonlinear lattices with saturable quintic nonlinearity, and systematically analyzes their existence and stability.

## Key findings

- Stable fundamental and dipole solitons identified.
- Stability regions mapped via numerical simulations.
- All stable solitons obey the Vakhitov-Kolokolov criterion.

## Abstract

The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a nonlinearlatticeandsaturationofthequinticnonlinearity. Thesystemsupportsthreespeciesofsolitons, namely, fundamental (even-parity) ones and dipole (odd-parity) modes of on- and off-site-centered types. Very narrow fundamental solitons are found in an approximate analytical form, and systematic results for very broad unstable and moderately broad partly stable solitons, including their existence and stability areas, are produced by means of numerical methods. Stability regions of the solitons are identified by means of systematic simulations. The stability of all the soliton species obeys the Vakhitov-Kolokolov criterion.