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