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Pré-Publication, Document De Travail Année : 2021

Instability of algebraic standing waves for nonlinear Schr\"odinger equations with triple power nonlinearities

Résumé

We consider the following triple power nonlinear Schrödinger equation: iut + ∆u + a 1 |u|u + a 2 |u| 2 u + a 3 |u| 3 u = 0. We are interested in algebraic standing waves i.e standing waves with algebraic decay above equation in dimensions n (n = 1, 2, 3). We prove the instability of these solutions in the cases DDF (we use abbreviation D: defocusing (a i < 0), F: focusing (a i > 0)) and DFF when n = 2, 3 and in the case DFF with a 2 < 32 15 √ 6 when n = 1. In the case DFD, we only obtain an existence result of algebraic solution in dimension one.
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Dates et versions

hal-03379146 , version 1 (14-10-2021)
hal-03379146 , version 2 (21-03-2022)

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Citer

Phan van Tin. Instability of algebraic standing waves for nonlinear Schr\"odinger equations with triple power nonlinearities. 2021. ⟨hal-03379146v1⟩
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