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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Mots clés : nonlinear Schrödinger equation, double power nonlinearity, standing waves, stability, orbital stability
Perla Kfoury 1 ; Stefan Le Coz 1 ; Tai-Peng Tsai 2
CC-BY 4.0
@article{CRMATH_2022__360_G8_867_0,
author = {Perla Kfoury and Stefan Le Coz and Tai-Peng Tsai},
title = {Analysis of stability and instability for standing waves of the double power one dimensional nonlinear {Schr\"odinger} equation},
journal = {Comptes Rendus. Math\'ematique},
pages = {867--892},
publisher = {Acad\'emie des sciences, Paris},
volume = {360},
year = {2022},
doi = {10.5802/crmath.351},
language = {en},
}
TY - JOUR AU - Perla Kfoury AU - Stefan Le Coz AU - Tai-Peng Tsai TI - Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation JO - Comptes Rendus. Mathématique PY - 2022 SP - 867 EP - 892 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.351 LA - en ID - CRMATH_2022__360_G8_867_0 ER -
%0 Journal Article %A Perla Kfoury %A Stefan Le Coz %A Tai-Peng Tsai %T Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation %J Comptes Rendus. Mathématique %D 2022 %P 867-892 %V 360 %I Académie des sciences, Paris %R 10.5802/crmath.351 %G en %F CRMATH_2022__360_G8_867_0
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. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 867-892. doi : 10.5802/crmath.351. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.351/
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