Stability analysis for extended models of gap solitary waves

A numerical linear stability analysis has been carried out for stationary spatially localized solutions of several systems of coupled nonlinear partial differential equations (PDE's) with two and more complex variables. These coupled PDE's have recently been discussed in the literature, mostly in the context of physical systems with a frequency gap in the dispersion relation of their linear excitations, and they are extensions of the Mills-Trullinger gap soliton model. Translational and oscillatory instabilities are identified, and their associated growth rates are computed as functions of certain parameters characterizing the solitary waves.