论文标题
在离散的klein-gordon方程中重新访问多润呼吸器：一种空间动力学方法
Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach
论文作者
论文摘要
我们考虑了离散的klein-gordon方程中多呼吸道结构的存在和光谱稳定性，包括软和硬对称势。为了获得分析结果，我们将系统投影到有限维的希尔伯特空间，该空间由任意$ m $的第一个$ m $ M $ M型模式组成。然后，在这个近似系统上，我们采用一种空间动力学方法，并使用Lin的方法从一系列单位单位呼吸器的一系列良好分离拷贝构造多呼吸器。然后，我们通过将光谱问题减少到矩阵方程式，将与此类多呼吸器状态的各个呼吸器之间的相互作用相关的浮子光谱定位。这些本本征的表达式是根据主要的呼吸器及其内核本本函数获得的，有限维系统的表达式，发现它们与数值浮雕光谱结果非常吻合。这补充了数值时间播放实验的结果，这些实验是使用光谱计算来解释的。
We consider the existence and spectral stability of multi-breather structures in the discrete Klein-Gordon equation, both for soft and hard symmetric potentials. To obtain analytical results, we project the system onto a finite-dimensional Hilbert space consisting of the first $M$ Fourier modes, for arbitrary $M$. On this approximate system, we then take a spatial dynamics approach and use Lin's method to construct multi-breathers from a sequence of well-separated copies of the primary, single-site breather. We then locate the eigenmodes in the Floquet spectrum associated with the interaction between the individual breathers of such multi-breather states by reducing the spectral problem to a matrix equation. Expressions for these eigenmodes for the approximate, finite-dimensional system are obtained in terms of the primary breather and its kernel eigenfunctions, and these are found to be in very good agreement with the numerical Floquet spectrum results. This is supplemented with results from numerical timestepping experiments, which are interpreted using the spectral computations.
