局域非线性对非线性Schrödinger方程的扰动

IF 1.4 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2025-08-28 DOI:10.1007/s11005-025-01984-3

Gong Chen, Jiaqi Liu, Yuanhong Tian

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引用次数: 0

摘要

我们重新研究了P. Deift和X. Zhou[8]提出的无限维可积系统的微扰理论，旨在提供一些关键\(L^\infty \)界和\(L^p\)先验估计的新的和更简单的证明。我们的证明强调了进一步理解聚焦问题，并扩展了对其他可积模型的适用性。作为一个具体应用，我们研究了局部高阶项对一维散焦三次非线性Schrödinger方程的扰动。我们引入改进的估计来控制扰动项的幂，并证明了扰动方程与完全可积非线性Schrödinger方程具有相同的长时间行为。

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perturbation of the nonlinear Schrödinger equation by a localized nonlinearity

We revisit the perturbative theory of infinite dimensional integrable systems developed by P. Deift and X. Zhou [8], aiming to provide new and simpler proofs of some key \(L^\infty \) bounds and \(L^p\) a priori estimates. Our proofs emphasizes a further step towards understanding focussing problems and extends the applicability to other integrable models. As a concrete application, we examine the perturbation of the one-dimensional defocussing cubic nonlinear Schrödinger equation by a localized higher-order term. We introduce improved estimates to control the power of the perturbative term and demonstrate that the perturbed equation exhibits the same long-time behavior as the completely integrable nonlinear Schrödinger equation.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.