Travelling lattice waves in a toy model of Lennard-Jones interaction
Travelling lattice waves in a toy model of Lennard-Jones interaction
复制标题
伦纳德-琼斯相互作用玩具模型中的行进晶格波
DOI：
10.1090/s0033-569x-2013-01320-4
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发表时间：
2013
影响因子：
0.8
通讯作者：
J. Zimmer
中科院分区：
文献类型：
--
作者：
Christine R. Venney;J. Zimmer
我们考虑一个无限晶格模型，其中粒子与最近邻（NN）和次近邻（NNN）相互作用; NN和NNN弹簧相互作用以模拟Lennard-Jones势。亚音速波同宿指数小周期振荡的存在性以及超音速周期解的存在性。证明依赖于同宿解的标准形和中心空间分析以及周期解的中心流形分析的方法。
We consider an infinite lattice model, where particles interact with nearest neighbour (NN) and next-to-nearest neighbours (NNN); the NN and NNN springs act against each other to mimic the Lennard-Jones potential. The existence of subsonic waves homoclinic to exponentially small periodic oscillations is shown as well as the existence of supersonic periodic solutions. The proofs rely on methods from normal form and centre space analysis for the homoclinic solutions and centre manifold analysis for the periodic solutions.