VIBRATION MODES OF A GAP SOLITON IN A NONLINEAR-OPTICAL MEDIUM

We analyze the dynamics of small internal vibrations in a two-componen t gap soliton. The general model considered describes at least three d ifferent nonlinear optical systems: a pair of waves coupled by the Bra gg scattering in a medium with a periodic grating, a twisted birefring ent fiber, and a dual-core asymmetric coupler. In all the cases the ma terial dispersion of the medium is neglected, but an effective dispers ion is induced by the linear coupling between the two modes. Employing the averaged Lagrangian variational technique we derive a system of o rdinary differential equations which approximates the dynamics of the gap soliton. We find three oscillation modes, which are composed of (m ixtures of) dilation-contraction of each component's width, and a rela tive translation of the two components. At certain values of the param eters the analysis yields spurious instabilities, which is a novel fai lure of the averaged Lagrangian variational technique.