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In this paper orbital stability of solutions of weakly coupled nonlinear Schrödinger equations is studied. It is proved that ground state solutions-scalar or vector ones-are orbitally stable , while bound states with Morse index strictly greater than one are not stable. Moreover, an instability result for large exponent in the nonlinearity is presented.
The semiclassical limit of a weakly coupled nonlinear focusing Schrödinger system in presence of a nonconstant potential is studied. The initial data is of the form (u 1 , u 2) with u i = r i x−˜x ε e i ε x·˜ξ , where (r 1 , r 2) is a real ground state solution, belonging to a suitable class, of an associated autonomous elliptic system. For ε sufficiently(More)
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