Dynamical stabilization of solitons in cubic-quintic nonlinear Schr\"odinger model

TL;DR

This paper demonstrates the dynamic stabilization of solitons in a one-dimensional cubic-quintic nonlinear Schrödinger model through strong nonlinearity management, confirmed by analytical and numerical methods.

Contribution

It introduces a method to achieve stable solitons in the cubic-quintic NLS model using strong nonlinearity management, aligning analytical predictions with numerical simulations.

Findings

Analytical predictions match numerical simulations.

Stable solitons can be achieved with strong nonlinearity management.

Collapse arrest is confirmed in the model.

Abstract

We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schr\"odinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the averaged cubic-quintic NLS equation and modified variational approach for the arrest of collapse coincide. The analytical results are confirmed by numerical simulations of one-dimensional cubic-quintic NLS equation with rapidly and strongly varying cubic nonlinearity coefficient.