等质量限制下双原子Fermi-Pasta-Ulam-Tsingou晶格中的微翼子行波
Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
摘要：
双原子Fermi-Pasta-Ulam-Tsingou（FPUT）晶格是由相同的非线性弹簧连接的交替粒子的无限长链。我们证明了微翼子行波在双原子FPUT晶格中的存在的限制作为两个交替的质量的比率接近1，在这一点上的双原子晶格减少到众所周知的单原子FPUT晶格。这些是行波，其轮廓在无穷远处渐近于小的周期性振荡，而不是像经典的孤波那样消失。我们产生这些micropteron波使用功能分析方法，最初是由于比尔，这是成功地部署在相关的长波和小质量双原子问题。与长波和小质量问题不同，这个等质量问题不是奇异摄动的，因此微翼子振荡的振幅不一定小到超过所有阶次（即，我们发现的行波不一定是纳米鳍）。这个等质量问题的核心挑战在于行波方程中隐藏的可解性条件，这体现在辅助前进-延迟微分方程的渐近正弦解（Jost解）的存在性和优良性质上。
英文摘要：
The diatomic Fermi-Pasta-Ulam-Tsingou (FPUT) lattice is an infinite chain of alternating particles connected by identical nonlinear springs. We prove the existence of micropteron traveling waves in the diatomic FPUT lattice in the limit as the ratio of the two alternating masses approaches 1, at which point the diatomic lattice reduces to the well-understood monatomic FPUT lattice. These are traveling waves whose profiles asymptote to a small periodic oscillation at infinity, instead of vanishing like the classical solitary wave. We produce these micropteron waves using a functional analytic method, originally due to Beale, that was successfully deployed in the related long wave and small mass diatomic problems. Unlike the long wave and small mass problems, this equal mass problem is not singularly perturbed, and so the amplitude of the micropteron's oscillation is not necessarily small beyond all orders (i.e., the traveling wave that we find is not necessarily a nanopteron). The central challenge of this equal mass problem hinges on a hidden solvability condition in the traveling wave equations, which manifests itself in the existence and fine properties of asymptotically sinusoidal solutions (Jost solutions) to an auxiliary advance-delay differential equation.
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