Abstract
The perturbation theory for an investigation of the stability of solitons in fiber array with a periodic change of a coupling constant is developed. The linear stability analysis is performed in an approximation of weak coupling within the framework of the system of dispersive discrete nonlinear Schr\"odinger equations. It is shown that the propagation of a soliton array in such a continuous-discrete system is unstable. The maximum of the growth rate of modulation instability is evaluated. Analyzing the mode structure of the corresponding eigenvalue problem in the vicinity of the threshold of instability it is found that in the system under consideration acoustical and optical unstable modes exist. Numerical calculations confirm the analytical results.
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