Abstract
We focus on the study of the stability properties of ground-states for the system of M coupled semilinear Schrodinger equations with power-type nonlinearities and couplings. Our results are generalizations of the theory for the single equation and the technique used is a simplification of the original one. Depending on the power of the nonlinearity, we may observe stability, instability and weak instability. We also obtain results for three distinct classes of bound-states, which is a special feature of the \({M \geqslant 2}\) case.
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