The Backlund transform, first developed in the context of differential geometry, has been classically used to obtain multi-soliton states in completely integrable infinite-dimensional dynamical systems. It has recently been used to study the stability of these special solutions. We offer here a dynamical perspective on the Backlund Transform, prove an abstract orbital stability theorem, and demonstrate its utility by applying it to the sine-Gordon equation and the Toda lattice.
- solitary waves,
- asymptotic stability,
- lattice solitons,
- energy space,
Available at: http://works.bepress.com/aaron_hoffman/18/