TY - JOUR
T1 - On the Korteweg–de Vries Limit for the Fermi–Pasta–Ulam System
AU - Hong, Younghun
AU - Kwak, Chulkwang
AU - Yang, Changhun
N1 - Funding Information:
This research of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2020R1A2C4002615). This work of the second author was supported by project France-Chile ECOS-Sud C18E06, the Ewha Womans University Research Grant of 2020, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A0106876811). This work of the third author was supported by the research grant of the Chungbuk National University in 2020 and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1C1C1005700). Part of this work was complete while the second author was visiting Chung-Ang University (Seoul, Republic of Korea). The second author acknowledges the warm hospitality of the institution.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature.
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 -