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

Younghun Hong; Chulkwang Kwak; Changhun Yang

doi:10.1007/s00205-021-01629-4

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

Younghun Hong, Chulkwang Kwak, Changhun Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 (Schneider and Wayne, In: International conference on differential equations, Berlin, 1999, World Sci. Publ, River Edge, NJ, Vol 1, 2, pp 390–404, 2000).

Original language	English
Pages (from-to)	1091-1145
Number of pages	55
Journal	Archive for Rational Mechanics and Analysis
Volume	240
Issue number	2
DOIs	https://doi.org/10.1007/s00205-021-01629-4
State	Published - May 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.

Access to Document

10.1007/s00205-021-01629-4

Cite this

@article{d00f3baa42254aaf8bae8441b5e3e723,

title = "On the Korteweg–de Vries Limit for the Fermi–Pasta–Ulam System",

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 (Schneider and Wayne, In: International conference on differential equations, Berlin, 1999, World Sci. Publ, River Edge, NJ, Vol 1, 2, pp 390–404, 2000).",

author = "Younghun Hong and Chulkwang Kwak and Changhun Yang",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.",

year = "2021",

month = may,

doi = "10.1007/s00205-021-01629-4",

language = "English",

volume = "240",

pages = "1091--1145",

journal = "Archive for Rational Mechanics and Analysis",

issn = "0003-9527",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - On the Korteweg–de Vries Limit for the Fermi–Pasta–Ulam System

AU - Hong, Younghun

AU - Kwak, Chulkwang

AU - Yang, Changhun

PY - 2021/5

Y1 - 2021/5

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=85102183836&partnerID=8YFLogxK

U2 - 10.1007/s00205-021-01629-4

DO - 10.1007/s00205-021-01629-4

M3 - Article

AN - SCOPUS:85102183836

SN - 0003-9527

VL - 240

SP - 1091

EP - 1145

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

ER -

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

Abstract

Bibliographical note

Access to Document

Fingerprint

Cite this