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Pré-Publication, Document De Travail Année : 2021

Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation

Résumé

For the double power one dimensional nonlinear Schrödinger equation, we establish a complete classification of the stability or instability of standing waves with positive frequencies. In particular, we fill out the gaps left open by previous studies. Stability or instability follows from the analysis of the slope criterion of Grillakis, Shatah and Strauss. The main new ingredients in our approach are a reformulation of the slope and the explicit calculation of the slope value in the zero-frequency case. Our theoretical results are complemented with numerical experiments.
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Dates et versions

hal-03476457 , version 1 (12-12-2021)
hal-03476457 , version 2 (30-12-2021)

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Perla Kfoury, Stefan Le Coz, Tai-Peng Tsai. Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation. 2021. ⟨hal-03476457v2⟩
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