Tetsu Mizumachi and Robert L Pego 2008 Nonlinearity 21 2099 doi:10.1088/0951-7715/21/9/011
Tetsu Mizumachi1 and Robert L Pego2
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We establish an asymptotic stability result for Toda lattice soliton solutions, by making use of a linearized Bäcklund 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.
37K40 Soliton theory, asymptotic behavior of solutions
37K60 Lattice dynamics (See also 37L60)
Issue 9 (September 2008)
Received 30 October 2007, in final form 11 July 2008
Published 7 August 2008
Tetsu Mizumachi and Robert L Pego 2008 Nonlinearity 21 2099
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