论文标题
矩形托里上一类阻尼梁的准周期性行进波
Quasi-periodic travelling waves for a class of damped beams on rectangular tori
论文作者
论文摘要
本文涉及一类光束方程，并在矩形托里上进行阻尼。当生成器满足某些关系时，通过排除两个模型参数的一些值，我们证明，这种模型以两个频率允许小幅度准周期性波动波解决方案，这是两个频率的两个旋转波解决方案的延续。该结果不仅适用于各向异性圆环，而且适用于各向异性圆环。该证明主要基于lyapunov--schmidt还原以及隐式函数定理。
This article concerns a class of beam equations with damping on rectangular tori. When the generators satisfy certain relationship, by excluding some value of two model parameters, we prove that such models admit small amplitude quasi-periodic travelling wave solutions with two frequencies, which are continuations of two rotating wave solutions with one frequency. This result holds not only for an isotropic torus, but also for an anisotropic torus. The proof is mainly based on a Lyapunov--Schmidt reduction together with the implicit function theorem.
