Center Stable Manifolds Around Line Solitary Waves of the Zakharov–Kuznetsov Equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-27 DOI:10.1007/s10884-023-10329-4

Yohei Yamazaki

引用次数: 1

Abstract

In this paper, we construct center stable manifolds of unstable line solitary waves for the Zakharov–Kuznetsov equation on \({\mathbb {R}} \times {\mathbb {T}}_L\) and show the orbital stability of the unstable line solitary waves on the center stable manifolds, which yields the asymptotic stability of unstable solitary waves on the center stable manifolds near by stable line solitary waves. The construction is based on the graph transform approach by Nakanishi and Schlag (SIAM J Math Anal 44:1175–1210, 2012). Applying the bilinear estimate on Fourier restriction spaces by Molinet and Pilod (Ann Inst H Poincaré Anal Non Lineaire 32:347–371, 2015) and modifying the mobile distance in Nakanishi and Schlag (2012), we construct a contraction map on the graph space.

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Zakharov-Kuznetsov方程线孤立波周围的中心稳定流形

本文对\({\mathbb {R}} \times {\mathbb {T}}_L\)上的Zakharov-Kuznetsov方程构造了不稳定线孤立波的中心稳定流形，并给出了不稳定线孤立波在中心稳定流形上的轨道稳定性，得到了不稳定线孤立波在中心稳定流形附近的渐近稳定性。该构造基于Nakanishi和Schlag (SIAM J Math Anal 44:11 175 - 1210, 2012)的图变换方法。应用Molinet和Pilod (Ann Inst H poincar Anal nonlineaire 32:34 47 - 371, 2015)对傅里叶限制空间的双线性估计，并修改Nakanishi和Schlag(2012)的移动距离，我们在图空间上构造了一个收缩映射。

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

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