Stability of the Periodic Toda Lattice in the Soliton Region
arXiv:0807.0244 · doi:10.1093/imrn/rnp077
Abstract
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the periodic (and slightly more generally of the quasi-periodic finite-gap) Toda lattice for decaying initial data in the soliton region. In addition, we show how to reduce the problem in the remaining region to the known case without solitons.
28 pages
References in corpus (8)
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Cited by in corpus (6)
- Stability of the periodic Toda lattice under short range perturbations
- Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds
- Long-Time Asymptotics of Perturbed Finite-Gap Korteweg-de Vries Solutions
- Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra
- Stability of the Periodic Toda Lattice: Higher Order Asymptotics
- Nonlinear steepest descent on a torus: A case study of the Landau-Lifshitz equation