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The Backlund Transform, first developed in the context of differentialgeometry, has been classically used to obtain multi-soliton states incompletely integrable infinite dimensional dynamical systems. It has recentlybeen used to study the stability of these special solutions. We offer here adynamical perspective on the Backlund Transform, prove an abstract orbitalstability theorem, and demonstrate its utility by applying it to thesine-Gordon equation and the Toda lattice.

Orbital Stability of Localized Structures via Backlund Transformations