We present modulation instability analysis including azimuthal perturbations of steady-state continuous wave (CW) propagation in multicore-fiber configurations with a central core. In systems with a central core, a steady CW evolution regime requires power-controlled phase matching, which offers interesting spatial-division applications. Our results have general applicability and are relevant to a range of physical and engineering systems, including high-power fiber lasers, optical transmission in multicore fiber, and systems of coupled nonlinear waveguides.
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