From resting to moving localized structures due to symmetry breaking

Summary form only given. Polarization fronts in intracavity second harmonic generation (SHG) are a representative example for localized structures or cavity solitons in dissipative systems. We use this particular example to demonstrate that nonlinear structures may destabilize due to symmetry breaking where a linear internal mode passes the translational mode. As a result a resting symmetric structure may transform into a moving asymmetric one. In the mean-field limit type II intracavity SHG is observed.