论文标题
标量FPU系统在2D方格上的KP-II近似
KP-II approximation for a scalar FPU system on a 2D square lattice
论文作者
论文摘要
我们考虑了正方形2D晶格上的标量Fermi-Pasta-Ulam（FPU）系统。可以通过多个尺度膨胀来得出Kadomtsev-PetviaShvili（KP-II）方程，以描述小幅度的单向长波，并缓慢变化横向调制。我们表明，KP-II近似对原始标量FPU系统的动力学做出了正确的预测。现有的近似结果扩展到波传播的任意方向。这项工作的主要新颖性是在应变变量中对FPU系统的分析中使用傅立叶变换。
We consider a scalar Fermi-Pasta-Ulam (FPU) system on a square 2D lattice. The Kadomtsev-Petviashvili (KP-II) equation can be derived by means of multiple scale expansions to describe unidirectional long waves of small amplitude with slowly varying transverse modulations. We show that the KP-II approximation makes correct predictions about the dynamics of the original scalar FPU system. An existing approximation result is extended to an arbitrary direction of wave propagation. The main novelty of this work is the use of Fourier transform in the analysis of the FPU system in strain variables.
