Korteweg--de Vries limit for the Fermi--Pasta--Ulam system

2019/12/27 by Younghun Hong, Hong, Younghun, Chulkwang Kwak +3
Mathematics · Physics and Astronomy · #35Q53 #37L60 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1912.11992

openalex publication_date 2019/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

Citations

• Strong Convergence for Discrete Nonlinear Schrödinger equations in the Continuum Limit

Related

• Periodic FPU system: Continuum limit to KdV via regularization and Fourier analysis
• Approximation of (some) FPUT lattices by KdV Equations
• Localized patterns and dispersive structures in two-dimensional Fermi-Pasta-Ulam lattices
• Long-Time approximations of small-amplitude, long-wavelength FPUT solutions
• Exact solutions in the FPU oscillator chain