Breather solutions in conservative and dissipative nonlinear Klein–Gordon lattices

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-29 DOI:10.1007/s11784-024-01106-x

Dirk Hennig

引用次数: 0

Abstract

We study time-periodic and spatially localised solutions (breathers) in general infinite conservative and dissipative nonlinear Klein–Gordon lattices. First, in the time-reversible (conservative) case, we give a concise proof of the existence of breathers not using the concept of the anticontinuous limit. The existence problem is converted into an operator equation for time-reversal initial conditions generating breather solutions. A nontrivial solution of this operator equation is established facilitating Schauder’s fixed point theorem. Afterwards, we prove the existence and uniqueness of breather solutions in damped and forced infinite nonlinear Klein–Gordon lattice systems utilising the contraction mapping principle.

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保守和耗散非线性克莱因-戈登网格中的呼吸解

我们研究一般无限保守和耗散非线性克莱因-戈登网格中的时间周期和空间局部解（呼吸器）。首先，在时间可逆（保守）情况下，我们给出了不使用反连续极限概念的呼吸器存在性的简明证明。存在性问题被转化为一个产生呼吸解的时间逆转初始条件的算子方程。这个算子方程的非微观解的建立促进了 Schauder 定点定理。随后，我们利用收缩映射原理证明了阻尼和强迫无限非线性克莱因-戈登晶格系统中呼吸解的存在性和唯一性。

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.