Orbital Stability of Localized Structures via Backlund Transformations
Dynamical Systems
2012-11-14 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1211.2836,
title = {Orbital Stability of Localized Structures via Backlund Transformations},
author = {A. Hoffman and C. E. Wayne},
journal= {arXiv preprint arXiv:1211.2836},
year = {2012}
}