The purpose of this paper is to construct small-amplitude breather solutions for a nonlinear Klein-Gordon equation posed on a periodic metric graph via spatial dynamics and center manifold reduction. The major difficulty occurs from the irregularity of the solutions. The persistence of the approximately constructed pulse solutions under higher order perturbations can be shown for two symmetric solutions.

中文翻译：

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周期度量图上非线性 Klein-Gordon 方程的呼吸器解的构造

本文的目的是通过空间动力学和中心流形约简为周期性度量图上提出的非线性 Klein-Gordon 方程构建小幅度呼吸器解。主要的困难来自于解的不规则性。对于两个对称解，可以显示在高阶扰动下近似构造的脉冲解的持久性。