Publication 07-CNA-08
**Asymptotic stability of Toda lattice solitons**

Tetsu Mizumachi

Kyushu University

Department of Mathematical Sciences

Faculty of Mathematics

mizumati@math.kyushu-u.ac.jp

and

Robert L. Pego

Department of Mathematical Sciences

Carnegie Mellon University

Pittsburgh, PA 15213

rpego@andrew.cmu.edu

**Abstract**: We establish an asymptotic stability result for Toda
lattice soliton solutions, by making use of a linearized Baecklund
transformation whose domain has codimension one. Combining a linear stability
result with a general theory of nonlinear stability by Friesecke and Pego for
solitary waves in lattice equations, we conclude that all solitons in the Toda
lattice are asymptotically stable in an exponentially weighted norm. In
addition, we determine the complete spectrum of an operator naturally
associated with the Floquet theory for these lattice solitons.

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