具有非局域相互作用的原子链中的KdV波
KdV waves in atomic chains with nonlocal interactions
摘要：
我们考虑具有非局域粒子相互作用的原子链，证明了近声波的存在。我们的结果和一般的证明策略都让人想起Friesecke和Pego关于最近邻相互作用链的KdV极限的开创性论文，但在以下两个方面有所不同：首先，我们允许更广泛的一类原子系统，因此必须用速度分布代替距离分布。其次，在渐近分析中，我们避免了详细的傅立叶极点特征的非局部积分算子，并采用压缩映射原理来解决最终的不动点问题。
英文摘要：
We consider atomic chains with nonlocal particle interactions and prove the existence of near-sonic solitary waves. Both our result and the general proof strategy are reminiscent of the seminal paper by Friesecke and Pego on the KdV limit of chains with nearest neighbor interactions but differ in the following two aspects: First, we allow for a wider class of atomic systems and must hence replace the distance profile by the velocity profile. Second, in the asymptotic analysis we avoid a detailed Fourier pole characterization of the nonlocal integral operators and employ the contraction mapping principle to solve the final fixed point problem.
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