The Bäcklund 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 Bäcklund Transform, prove an abstract orbital stability theorem, and demonstrate its utility by applying it to the sine-Gordon equation and the Toda lattice.
"Orbital stability of localized structures via Bäcklund transfomations." Differential Integral Equations 26 (3/4) 303 - 320, March/April 2013. https://doi.org/10.57262/die/1360092826