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arXiv · 1405.5549

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

Benedetta Noris·Hugo Tavares·Gianmaria Verzini
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Abstract

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 of 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.

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Benedetta Noris, Hugo Tavares, Gianmaria Verzini. 2014-05-21. Stable solitary waves with prescribed $L^2$-mass for the cubic Schrödinger system with trapping potentials. https://arxiv.org/abs/1405.5549

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