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Stable solitary waves with prescribed $L^2$-mass for the cubic Schrödinger system with trapping potentials

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  • For the cubic Schrödinger system with trapping potentials in $\mathbb{R}^N$, $N\leq3$, or in bounded domains, we investigate the existence and the orbital stability of standing waves having components with prescribed $L^2$-mass. We provide a variational characterization of such solutions, which gives information on the stability through a condition of Grillakis-Shatah-Strauss type. As an application, we show existence of conditionally orbitally stable solitary waves when: a) the masses are small, for almost every scattering lengths, and b) in the defocusing, weakly interacting case, for any masses.
    Mathematics Subject Classification: Primary: 35C08, 35Q55, 35J50; Secondary: 35B40.

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