Existence of multi-solitons for the focusing Logarithmic Non-Linear Schrödinger Equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-05-01 DOI:10.1016/j.anihpc.2020.09.002

Guillaume Ferriere

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引用次数: 15

Abstract

We consider the logarithmic Schrödinger equation (logNLS) in the focusing regime. For this equation, Gaussian initial data remains Gaussian. In particular, the Gausson - a time-independent Gaussian function - is an orbitally stable solution. In this paper, we construct multi-solitons (or multi-Gaussons) for logNLS, with estimates in $H^{1} \cap F (H^{1})$ . We also construct solutions to logNLS behaving (in $L^{2}$ ) like a sum of N Gaussian solutions with different speeds (which we call multi-gaussian). In both cases, the convergence (as $t \to \infty$ ) is faster than exponential. We also prove a rigidity result on these constructed multi-gaussians and multi-solitons, showing that they are the only ones with such a convergence.

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聚焦对数非线性Schrödinger方程多孤子的存在性

我们在聚焦区考虑对数Schrödinger方程(logls)。对于这个方程，高斯初始数据仍然是高斯的。特别地，高斯函数——一个与时间无关的高斯函数——是一个轨道稳定解。在本文中，我们构造了logNLS的多孤子(或多高斯子)，其估计在H1∩F(H1)。我们还构造了logNLS的解，其行为(在L2中)类似于N个不同速度的高斯解的和(我们称之为多高斯)。在这两种情况下，收敛(当t→∞)都比指数更快。我们还证明了这些构造的多高斯和多孤子的一个刚性结果，表明它们是唯一具有这种收敛性的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.