Article
Orbital Stability of Localized Structures via Backlund Transformations
Differential and Integral Equations
(2013)
Abstract
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.
Keywords
- solitary waves,
- asymptotic stability,
- lattice solitons,
- energy space,
- equations,
- manifolds
Disciplines
Publication Date
March, 2013
Citation Information
Aaron Hoffman and C. E. Wayne. "Orbital Stability of Localized Structures via Backlund Transformations" Differential and Integral Equations Vol. 26 Iss. 3-4 (2013) Available at: http://works.bepress.com/aaron_hoffman/18/
© 2013 Khayyam Publishing Inc. This article was published in Differential and Integral Equations, vol. 26, iss. 3-4, p. 303-320 and may be found here.