Korteweg--de Vries limit for the Fermi--Pasta--Ulam system
Analysis of PDEs
2019-12-30 v1
Abstract
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 [45].
Keywords
Cite
@article{arxiv.1912.11992,
title = {Korteweg--de Vries limit for the Fermi--Pasta--Ulam system},
author = {Younghun Hong and Chulkwang Kwak and Changhun Yang},
journal= {arXiv preprint arXiv:1912.11992},
year = {2019}
}
Comments
48page