Multibreather and Vortex Breather stability in Klein-Gordon Lattices: Equivalence between Two Different Approaches
Multibreather and Vortex Breather stability in Klein-Gordon Lattices: Equivalence between Two Different Approaches
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克莱因-戈登格子中的多重呼吸器和涡旋呼吸器稳定性：两种不同方法之间的等效性
DOI：
10.1142/s0218127411029690
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
J. Archilla
中科院分区：
文献类型：
--
作者：
J. Cuevas;V. Koukouloyannis;P. Kevrekidis;J. Archilla
在这项工作中，我们重新审视了多重呼吸器配置的稳定性问题，即在非耦合振荡器的反连续极限处具有多个激发位点的离散呼吸器。我们提出了两种方法，基于奥布里能带方法和麦凯有效哈密顿方法，对这种指数局域于空间、时间周期轨道的线性稳定性分析的Floquet乘子进行定量预测，并证明通过对奥布里能带理论中能带的形式做出适当的假设，它们的结论是等价的。随后，我们通过一系列案例展示了这些方法的实用性，包括在具有莫尔斯势的线性耦合振荡器晶格的情况下以及在离散 phi4 模型中的一维多呼吸器和二维涡流呼吸器。
In this work, we revisit the question of stability of multibreather configurations, i.e. discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We present two methods that yield quantitative predictions about the Floquet multipliers of the linear stability analysis around such exponentially localized in space, time-periodic orbits, based on the Aubry band method and the MacKay effective Hamiltonian method, and prove that by making the suitable assumptions about the form of the bands in the Aubry band theory, their conclusions are equivalent. Subsequently, we showcase the usefulness of the methods through a series of case examples including one-dimensional multi-breathers, and two-dimensional vortex breathers in the case of a lattice of linearly coupled oscillators with the Morse potential and in that of the discrete ϕ4 model.