论文标题
粒子链中的1：2：4共振
The 1:2:4 resonance in a particle chain
论文作者
论文摘要
我们在圆形构型中考虑了四个质量，它们具有最近的邻次相互作用，从而推广了空间周期性的fermi-pasta- ulam链，其中所有质量均等。我们确定产生$ 1 {：} 2 {：} 4 $〜共振的质量比 - 通常是按立方顺序排列的正常形式。将四个质量中的两个相等地占据，可以保留完全对称的fermi-pasta-ulam链的离散对称性，并产生可集成的正常形式近似。如果潜在的立方术语消失，则后者也是如此。我们将这些情况放在上下文中并分析所得的动态，包括$ 1 {：} 2 {：} 4 $〜共振的$ 1 {：} 2 {：}。
We consider four masses in a circular configuration with nearest-neighbour interaction, generalizing the spatially periodic Fermi--Pasta--Ulam-chain where all masses are equal. We identify the mass ratios that produce the $1{:}2{:}4$~resonance --- the normal form in general is non-integrable already at cubic order. Taking two of the four masses equal allows to retain a discrete symmetry of the fully symmetric Fermi--Pasta--Ulam-chain and yields an integrable normal form approximation. The latter is also true if the cubic terms of the potential vanish. We put these cases in context and analyse the resulting dynamics, including a detuning of the $1{:}2{:}4$~resonance within the particle chain.
