Travelling waves in discrete nonlinear systems with non-nearest neighbour interactions
Travelling waves in discrete nonlinear systems with non-nearest neighbour interactions
复制标题
具有非最近邻相互作用的离散非线性系统中的行波
DOI：
10.1088/0951-7715/22/11/001
复制
发表时间：
2009
期刊：
影响因子：
1.7
通讯作者：
Y. Sire
中科院分区：
文献类型：
--
作者：
R. Calleja;Y. Sire
本文的目的是在具有非近邻相互作用的一维扩展晶格模型中提供行波的构造。这些模型主要来自固态物理，在能量传播机制中起着重要作用。我们专注于克莱因-戈登链的扩展版本，即每个粒子嵌入到一个非谐波势中，并与它们的第一个和第二个邻居线性耦合。我们利用约简到有限维中心流形的技术证明了几种类型行波的存在性，并研究了与第二近邻的相互作用所起的作用。
The aim of this paper is to provide a construction of travelling waves in an extended one-dimensional lattice model with non-nearest neighbour interactions. These models, coming mainly from solid state physics, are known to play an important role in the mechanisms of propagation of energy. We focus on an extended version of the Klein–Gordon chains, i.e. each particle is embedded into an an-harmonic potential and linearly coupled to their first and second neighbours. We use the technique of reduction to a finite-dimensional centre manifold to prove the existence of travelling waves of several types and investigate the role played by the interaction to second nearest neighbours.