凸FPU链中的单模波列和孤子
Unimodal wave trains and solitons in convex FPU chains
摘要：
我们考虑原子链与最近邻相互作用和研究周期和同宿行波，这被称为波列和孤子，分别。我们的主要结果是一个新的存在性证明，它依赖于约束最大化的势能，并利用改进算子的不变性。该方法仅限于凸相互作用势，但细化的标准结果，因为它提供了存在的行波单峰，甚至轮廓函数。此外，我们还讨论了波列的数值逼近和完全局域化，并表明当周期长度趋于无穷大时，波列收敛为孤子。
英文摘要：
We consider atomic chains with nearest neighbour interactions and study periodic and homoclinic travelling waves which are called wave trains and solitons, respectively. Our main result is a new existence proof which relies on the constrained maximisation of the potential energy and exploits the invariance properties of an improvement operator. The approach is restricted to convex interaction potentials but refines the standard results as it provides the existence of travelling waves with unimodal and even profile functions. Moreover, we discuss the numerical approximation and complete localization of wave trains, and show that wave trains converge to solitons when the periodicity length tends to infinity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
