On the Korteweg-de Vries Limit for the Fermi-Pasta-Ulam System

被引：10

作者：

Hong, Younghun ^{[1
]}

Kwak, Chulkwang ^{[2
]}

Yang, Changhun ^{[3
]}

机构：

[1] Chung Ang Univ, Dept Math, Seoul 06974, South Korea

[2] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea

[3] Chungbuk Natl Univ, Dept Math, Cheongju 28644, South Korea

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2021年 / 240卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

GLOBAL WELL-POSEDNESS; SOLITARY WAVES; FPU LATTICES; DEVRIES EQUATION; CAUCHY-PROBLEM; ILL-POSEDNESS; KDV; APPROXIMATION; MODULATION; STABILITY;

D O I：

10.1007/s00205-021-01629-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop dispersive PDE techniques for the Fermi-Pasta-Ulam (FPU) system with infinitely many oscillators, and we show that general solutions to the infinite FPU system can be approximated by counter-propagating waves governed by the Korteweg-de Vries (KdV) equation as the lattice spacing approaches zero. Our result not only simplifies the hypotheses but also reduces the regularity requirement in the previous study (Schneider and Wayne, In: International conference on differential equations, Berlin, 1999, World Sci. Publ, River Edge, NJ, Vol 1, 2, pp 390-404, 2000).

引用

页码：1091 / 1145

页数：55

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