  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.
