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arXiv · 1211.2836

Orbital Stability of Localized Structures via Backlund Transformations

A. Hoffman·C. E. Wayne
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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.

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A. Hoffman, C. E. Wayne. 2012-11-12. Orbital Stability of Localized Structures via Backlund Transformations. https://arxiv.org/abs/1211.2836

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