Korteweg–de Vries and Fermi–Pasta–Ulam–Tsingou: asymptotic integrability of quasi unidirectional waves

@article{Gallone2021KortewegdeVA,
  title={Korteweg–de Vries and Fermi–Pasta–Ulam–Tsingou: asymptotic integrability of quasi unidirectional waves},
  author={Matteo Gallone and Antonio Ponno and Bob W. Rink},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
In this paper we construct a higher order expansion of the manifold of quasi unidirectional waves in the Fermi–Pasta–Ulam–Tsingou (FPUT) chain. We also approximate the dynamics on this manifold. As perturbation parameter we use h 2 = 1/n 2, where n is the number of particles of the chain. It is well known that the dynamics of quasi unidirectional waves is described to first order by the Korteweg–de Vries (KdV) equation. Here we show that the dynamics to second order is governed by a combination… 
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References

SHOWING 1-10 OF 49 REFERENCES
Normal Form and Solitons, in A.V
  • Mikhailov (ed.), Integrability,
  • 2009
Normal form and solitons Integrability (Lecture Notes in Physics vol 767) ed A V Mikhailov (Berlin: Springer
  • 2009
On stochastization of one-dimensional chains of nonlinear oscillators
1. Fermi, Pasta, and Ulam performed in 1954 a series of numerical experiments aimed at ascertaining how randomization and the transition to a uniform en­ ergy distribution take place in dynamic
Proof of Nishida's Conjecture on Anharmonic Lattices
We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal
Ponno A and Ponno A 2021 Understanding the FPU state in FPU-like models Math. Eng
  • 2021
Understanding the FPU state in FPU–like models
TLDR
The aim of this paper is 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.
Adiabatic Invariants for the FPUT and Toda Chain in the Thermodynamic Limit
We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by $N \gg 1$ particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature
Hamiltonian Studies on Counter-Propagating Water Waves
We use a Hamiltonian normal form approach to study the dynamics of the water wave problem in the small-amplitude long-wave regime (KdV regime). If $$\mu $$ μ is the small parameter corresponding to
and s
The Fermi–Pasta–Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents
FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual $$\beta $$β-model, perturbations of Toda include
...
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2
3
4
5
...