Quadratic cavity solitons-the up-conversion case

We derive mean-field equations for intra-cavity second-harmonic generation. Based on this model, we show that a variety of quadratic cavity solitons can exist. Highly symmetric and resting cavity solitons originate from primary bifurcations of the underlying stationary plane wave solutions. For certain control parameters, these solutions may undergo a secondary bifurcation leading to symmetry-reduced and/or moving/breathing quadratic cavity solitons. In particular, we predict for the first time the existence of triangular cavity solitons and derive a criterion for an nonequilibrium Ising-Bloch transition