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arXiv · 1208.5680

Beating effects in cubic Schr\"odinger systems and growth of Sobolev norms

Benoît Grébert·Éric Paturel·Laurent Thomann
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Abstract

We consider a system of coupled cubic Schr\"odinger equations. We prove that there exists a beating effect, i.e. an energy exchange between different modes. This construction may be transported to the linear time-dependent Schr\"odinger equation: we build solutions such that their Sobolev norms grow logarithmically. All these results are stated for large but finite times.

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Benoît Grébert, Éric Paturel, Laurent Thomann. 2012-08-28. Beating effects in cubic Schr\"odinger systems and growth of Sobolev norms. https://arxiv.org/abs/1208.5680

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