Stability analysis for extended models of gap solitary waves

A numerical linear stability analysis has been carried out for stationary s patially localized solutions of several systems of coupled nonlinear partia l differential equations (PDE's) with two and more complex variables. These coupled PDE's have recently been discussed in the literature, mostly in th e context of physical systems with a frequency gap in the dispersion relati on of their linear excitations, and they are extensions of the Mills-Trulli nger gap soliton model. Translational and oscillatory instabilities are ide ntified, and their associated growth rates are computed as functions of cer tain parameters characterizing the solitary waves.