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

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. Avariational approximation (VA) is used to predict dependence of the soliton's propagation constant on the norm, and the respective stability regions are identified using the Vakhitov-Kolokolov criterion. Analytical results obtained by means of the VA are corroborated by numerical simulations of the cubic-quintic-septimal nonlinear Schrodinger equation.