Conditional stability of multi-solitons for the 1D NLKG equation with double power nonlinearity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-01 DOI:10.1016/j.anihpc.2020.11.008

Xu Yuan

引用次数: 0

Abstract

We consider the one-dimensional nonlinear Klein-Gordon equation with a double power focusing-defocusing nonlinearity $\partial_{t}^{2} u - \partial_{x}^{2} u + u - | u |^{p - 1} u + | u |^{q - 1} u = 0, on [0, \infty) \times R,$ where $1 < q < p < \infty$ . The main result states the stability in the energy space $H^{1} (R) \times L^{2} (R)$ of the sums of decoupled solitary waves with different speeds, up to the natural instabilities. The proof is inspired by the techniques developed for the generalized Korteweg-de Vries equation and the nonlinear Schrödinger equation in a similar context by Martel, Merle and Tsai [14], [15]. However, the adaptation of this strategy to a wave-type equation requires the introduction of a new energy functional adapted to the Lorentz transform.

查看原文本刊更多论文

一维双幂非线性NLKG方程多孤子的条件稳定性

我们考虑一维非线性Klein-Gordon方程，该方程具有双焦度聚焦散焦非线性？t2u−？x2u+u−| u | p−1u+| u | q−1u=0，关于[0，∞）×R，其中1<；q<；p<；∞。主要结果表明了不同速度的解耦孤立波之和在能量空间H1（R）×L2（R）中的稳定性，直至自然不稳定性。该证明受到了Martel、Merle和Tsai[14]在类似情况下为广义Korteweg-de-Vries方程和非线性Schrödinger方程开发的技术的启发，[15]。然而，要使这种策略适应波动型方程，需要引入一种适应洛伦兹变换的新能量泛函。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.