Int. Math. Res. Not. 2009:21, 3996-4031 (2009) [DOI: 10.1093/imrn/rnp077]
Stability of the Periodic Toda Lattice in the Soliton Region
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.