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

  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},
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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