Instability of continuous waves and rotating solitons in waveguide arrays

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Abstract
The effect of a nonvanishing transverse wave vector on the stability of continuous waves and temporal solitons which propagate in an array of nonlinear optical waveguides is studied both analytically and numerically. We derive analytical expressions for the domain of existence as well as the gain of modulational instability of moving continuous waves. Because the transverse wave vector controls the ``discrete diffraction'' the stability behavior critically depends on this quantity. By employing the perturbation theory near neutrally stable modes it is shown that there are two different scenarios for the evolution of modulationally unstable soliton arrays. The transverse wave vector of the unstable solution determines which kind of instability develops. Numerical calculations confirm the analytical results.