Long-time asymptotics of the periodic Toda lattice under short-range perturbations

@article{Kamvissis2012LongtimeAO,
  title={Long-time asymptotics of the periodic Toda lattice under short-range perturbations},
  author={Spyridon Kamvissis and Gerald Teschl},
  journal={Journal of Mathematical Physics},
  year={2012},
  volume={53},
  pages={073706}
}
We compute the long-time asymptotics of periodic (and slightly more generally of algebro-geometric finite-gap) solutions of the doubly infinite Toda lattice under a short-range perturbation. In particular, we prove that the perturbed lattice asymptotically approaches a modulated lattice. More precisely, let g be the genus of the hyperelliptic curve associated with the unperturbed solution. We show that, apart from the phenomenon of solitons travelling in a quasi-periodic background, the n/t… 

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