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Mathematics > Analysis of PDEs
Title: Birkhoff normal form in low regularity for the nonlinear quantum harmonic oscillator
(Submitted on 23 Nov 2022 (v1), last revised 28 Mar 2024 (this version, v2))
Abstract: Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as multiplicative potentials, in a way that the linear frequencies satisfy a non-resonance condition. More precisely, we prove that for almost all potentials $V$, the low modes of the solution are almost preserved for very long times.
Submission history
From: Charbella Abou Khalil [view email][v1] Wed, 23 Nov 2022 16:08:34 GMT (40kb)
[v2] Thu, 28 Mar 2024 09:41:07 GMT (42kb)
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