Curvature dynamics and stability of topological solitons in the optical parametric oscillator

The first analytic verification of the stability of topological solitons co rresponding to wave-front solutions of the optical parametric oscillator is given. A translational invariance allows perturbations to the system to sh ift the front position without affecting the underlying exponential stabili ty of the fronts themselves. For the two-dimensional problem with a positiv e O(1) signal detuning, the front curvature is shown to be governed by a he at equation, so that the only stable topological solitons supported must be stripes. O 1999 Optical Society of America [S0740-3224(99)02411-X].