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We report the existence of a new family of stable stationary solitons in the one-dimensional cubicquintic complex Ginzburg-Landau equation with the viscosity term. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We find the bistable solitons in the presence of the small viscosity term.We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons. We conclude that the existence condition obtained by the paraxial method may serve as physically more reliable initial condition for stable stationary soliton propagation in the optical system modeled by the one-dimensional cubic-quintic complex Ginzburg-Landau equation with the viscosity term, of which analytical solution is not obtainable with all nonzero parameters.

Existence Conditions for Stable Stationary Solitons of the Cubic-Quintic Complex Ginzburg-Landau Equation with a Viscosity Term