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. A variational 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 Schrödinger equation.