Understanding the FPU state in FPU-like models

Mathematics in Engineering

卷:3

Giancarlo Benettin¹  Antonio Ponno¹ 

[1] Università degli Studi di Padova, Dipartimento di Matematica "Tullio Levi-Civita", Via Trieste 63, 35121 Padova, Italy;

关键词: fpu problem;    toda model;    integrability;    scaling laws;    toda actions;   

DOI  :  10.3934/mine.2021025

来源: DOAJ

【 摘 要 】

Many papers investigated, in a variety of ways, the so-called "FPU state" in the Fermi-Pasta-Ulam model, namely the state, intermediate between the initial state and equipartition, that the system soon reaches if initially one or a few long-wavelength normal modes are excited. The FPU state has been observed, in particular, to obey a few characterizing scalings laws. The aim of this paper is twofold: First, reviewing and commenting the literature on the FPU state, suggesting a possible way to organize it. Second, contributing to a better understanding of the FPU state by studying the similar state in the Toda model, which provides, as is known, the closest integrable approximation to FPU. As a new tool, we analyze the dimensionality of Toda invariant tori in states corresponding to the FPU state, and observe it obeys the main scaling law characterizing the FPU state.

【 授权许可】

Unknown