Standing waves of nonlinear Schrödinger systems with all attractive forces

IF 1.4 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2026-06-09 DOI:10.1112/jlms.70594

Jaeyoung Byeon

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引用次数: 0

Abstract

Since the pioneering work of Lin and Wei on nonlinear Schrödinger systems of $n$ components with interaction forces $a_{i j}$ between the $i$ -th and $j$ -th components for $1 ⩽ i, j ⩽ n$ , there have been numerous further developments in many directions. However, even in the simplest case where all interaction forces are attractive, (which corresponds to $a_{i j} ⩾ 0$ for every $1 ⩽ i, j ⩽ n$ ), a systematic approach to finding a solution with all positive components is still not known. In the special case $n = 2$ , a very systematic approach has been developed by Ambrosetti and Colorado. In this paper, we review the fundamental works by Lin–Wei and Ambrosetti–Colorado and further developments.

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具有所有吸引力的非线性Schrödinger系统的驻波

自Lin和Wei的开创性工作以来，n个$n$组件的非线性Schrödinger系统与i之间的相互作用力a i j $a_{ij}$$i$-th和j $j$ - 1≤I, j≤n $1\leqslant i,j\leqslant n$的分量，在许多方向上有了许多进一步的发展。然而，即使在最简单的情况下，所有的相互作用力都是吸引的，(对应于每1≤I的I j或0 $a_{ij} \geqslant 0$，J < n $1\leqslant i,j\leqslant n$)，一种寻找所有正分量的解的系统方法仍然未知。在特殊情况n = 2 $n=2$中，Ambrosetti和Colorado开发了一种非常系统的方法。本文回顾了林伟和ambroseti - colorado的基本工作及其进一步发展。

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

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.