In this note, we present a result established in [BGR24] where we prove that nonlinear Schrödinger equations on the circle, without external parameters, admit plenty of infinite dimensional non resonant invariant tori, or equivalently, plenty of almost periodic solutions. Our aim is to propose an extended sketch of the proof, emphasizing the new points which have enabled us to achieve this result.
@article{SLSEDP_2024-2025____A4_0,
author = {Joackim Bernier and Beno{\^\i}t Gr\'ebert},
title = {On almost periodic solutions to {NLS} without~external~parameters},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:10},
pages = {1--15},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2024-2025},
doi = {10.5802/slsedp.177},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.177/}
}
TY - JOUR AU - Joackim Bernier AU - Benoît Grébert TI - On almost periodic solutions to NLS without external parameters JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:10 PY - 2024-2025 SP - 1 EP - 15 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.177/ DO - 10.5802/slsedp.177 LA - en ID - SLSEDP_2024-2025____A4_0 ER -
%0 Journal Article %A Joackim Bernier %A Benoît Grébert %T On almost periodic solutions to NLS without external parameters %J Séminaire Laurent Schwartz — EDP et applications %Z talk:10 %D 2024-2025 %P 1-15 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.177/ %R 10.5802/slsedp.177 %G en %F SLSEDP_2024-2025____A4_0
Joackim Bernier; Benoît Grébert. On almost periodic solutions to NLS without external parameters. Séminaire Laurent Schwartz — EDP et applications (2024-2025), Exposé no. 10, 15 p. doi : 10.5802/slsedp.177. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.177/
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