Effective Hamiltonian for travelling discrete breathers
Effective Hamiltonian for travelling discrete breathers
复制标题
用于旅行离散呼吸的有效哈密顿量
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Sepulchre
中科院分区：
文献类型：
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作者：
R. MacKay;J. Sepulchre
一般的哈密顿振子链可能不支持精确的离散呼吸子。然而，看起来像移动离散呼吸子一段时间的解决方案在数值中并不难观察。在本文中，我们提出了一个抽象的框架来描述近似的运动离散呼吸子的哈密顿链的振荡器。该方法是基于一个有效的哈密顿量的建设，使一个描述的动态的移动呼吸器的自由度的翻译。对近似动力学的误差估计也进行了研究。Peierls-Nabarro势垒的概念可以在这个框架中得到明确。我们用两个简单的例子来说明这种方法，即萨莱诺模型，它插在Ablowitz-Ladik晶格和离散的非线性薛定谔系统之间，和费米-Pasta-Ulam链。
Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls–Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz–Ladik lattice and the discrete nonlinear Schrodinger system, and the Fermi–Pasta–Ulam chain.