Dispersion-induced transition towards dynamical parametric solitary waves

Summary form only given. Parametric solitary waves (such as, e.g., the self-induced transparency soliton) result from a balance between energy exchanges and the group velocity difference between the interacting waves. Apart from the group velocity difference, dispersion effects on the interacting waves has been systematically ignored in previous theoretical studies of parametric solitary waves. We show here that this systematic omission is not valid and that even very weak dispersion can drastically alter the parametric solitary waves dynamics yielding the novel concept of dynamical parametric solitary waves.