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Construction of Quasi-periodic solutions with the same Gevrey index as nonlinear terms in Multi-Dimensional NLS

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Zuhong You, Xiaoping Yuan

Analysis of PDEs · Submitted 15 Oct 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of quasi-periodic solutions that are Gevrey smooth with the same Gevrey index as the nonlinearity.

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arXiv ID2410.11249 (version 2)
Pith IDBA3BISZK, Pith's permanent record of this paper and its review
CitationXiaoping Yuan, Zuhong You. "Construction of Quasi-periodic solutions with the same Gevrey index as nonlinear terms in Multi-Dimensional NLS." arXiv:2410.11249 (2024). https://pith.science/paper/BA3BISZK
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,374 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.25 · compares with prior results 0.09 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We investigate the persistency of quasi-periodic solutions to multi-dimensional nonlinear Schr\"{o}dinger equations (NLS) involving Gevrey smooth nonlinearity with an arbitrary Gevrey index $\alpha>1$. By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of quasi-periodic solutions that are Gevrey smooth with the same Gevrey index as the nonlinearity.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We investigate the persistency of quasi-periodic solutions to multi-dimensional nonlinear Schr\"{o}dinger equations (NLS) involving Gevrey smooth nonlinearity with an arbitrary Gevrey index $\alpha>1$. contribution 0.67 0.76 0.10 asserted 0.66
s1 By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of quasi-periodic solutions that are Gevrey smooth with the same Gevrey index as the nonlinearity. result 0.64 0.96 0.91 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We investigate the persistency of quasi-periodic solutions to multi-dimensional nonlinear Schr\"{o}dinger equations (NLS) involving Gevrey smooth nonlinearity with an arbitrary Gevrey index $\alpha>1$. By applying the Craig-Wayne-Bourgain (CWB) method, we establish the existence of quasi-periodic solutions that are Gevrey smooth with the same Gevrey index as the nonlinearity.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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  • By collecting the functions ${σ_j(λ,λ')}$ for all $β$ and extending $σ_j$ to $I_0×I_0$ ( see Appendix B in [ref] for Lipschitz extension, for example), we obtain at most $M_1^b+d$ Lipschitz functions ${σ_j=σ_j(λ,λ')}$ such that [equation] The reason for extending $σ_j$ is that the above construction is carried out in an an $M_1^-1 e^-2 M_0$-neighborhood of $(λ,λ',σ)$.

    A lecture on the classical KAM theorem · The matrices $T_N^σ$ and its estimation · 0.97

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