Stability conditions for one-dimensional optical solitons in cubic-quintic-septimal media

TL;DR

This paper investigates the stability of one-dimensional optical solitons in media with up to seventh-order nonlinearities, identifying stability regions and collapse conditions through analytical and numerical methods.

Contribution

It provides the first comprehensive analysis of stability conditions for solitons in cubic-quintic-septimal media, combining variational approximation with numerical simulations.

Findings

Well-defined stability regions exist even with all focusing nonlinearities.

Conditions for supercritical collapse are identified.

Analytical predictions agree with numerical simulations.

Abstract

Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear terms are focusing. Conditions for onset of the supercritical collapse of the optical beam are identified too. A variational approximation is used to predict dependence of the soliton propagation constant on the norm, and respective stability regions are identified using the Vakhitov-Kolokolov criterion. Analytical results obtained by means of the variational approximation are corroborated by numerical simulations of the cubic-quintic-septimal nonlinear Schroedinger equation.