A normal form for nonlinear resonance of embedded solitons

A normal form for nonlinear resonance of embedded solitons is derived for a coupled twowave system that generalizes the secondharmonicgenerating model. This wave system is nonHamiltonian in general. An embedded soliton is a localized mode of the nonlinear system that coexists with the linear wave spectrum. It occurs as a result of a codimensionone bifurcation of nonlocal wave solutions. Nonlinearity couples the embedded soliton and the linear wave spectrum and induces a onesided radiationdriven decay of embedded solitons. The normal form shows that the embedded soliton is semistable, i.e. it survives under perturbations of one sign, but is destroyed by perturbations of the opposite sign. When a perturbed embedded soliton sheds continuous wave radiation, the radiation amplitude is generally not minimal, even if the wave system is Hamiltonian. The results of the analytical theory are confirmed by numerical computations.