Article

**Int. Math. Res. Not. 2009:21, 3996-4031 (2009)**[DOI: 10.1093/imrn/rnp077]

## Stability of the Periodic Toda Lattice in the Soliton Region

### Helge Krüger and Gerald Teschl

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.

** MSC2000:** Primary 37K40, 37K45; Secondary 35Q15, 37K20

**Keywords:** *Riemann-Hilbert problem, Toda lattice, Solitons*

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