Résumé
A method is proposed to solve the challenging problem of determining the supratransmission threshold (onset of insability of harmonic boundary driving inside a band gap) in multicomponent non-integrable nonlinear systems. It is successfully applied to the degenerate three-wave resonant interaction in a birefrigent quadratic medium where the process generates spatial gap solitons. No analytic expression is known for such nonlinear solitary waves showing the broad applicability of the method to nonlinear systems.