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

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10 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

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

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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).",

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AU - Kwak, Chulkwang

AU - Yang, Changhun

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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).

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

Abstract

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