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Journées équations aux dérivées partielles

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Victor Vilaça Da Rocha
Emphasizing nonlinear behaviors for cubic coupled Schrödinger systems
Journées équations aux dérivées partielles (2017), Exp. No. 9, 13 p., doi: 10.5802/jedp.659
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Résumé - Abstract

The purpose of this note is to propose a study of various nonlinear behaviors for a system of two coupled cubic Schrödinger equations with small initial data. Depending on the choice of the spatial domain, we highlight different examples of nonlinear behaviors. The goal is to mix the approaches of the study on the torus (with a truly nonlinear behavior) and of the study on the real line (with an infinite behavior) in order to obtain on the product space $\mathbb{R}\times \mathbb{T}$ a truly nonlinear behavior in infinite time.

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