Differential and Integral Equations

Orbital stability of localized structures via Bäcklund transfomations

A. Hoffman and C.E. Wayne

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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.

Article information

Differential Integral Equations, Volume 26, Number 3/4 (2013), 303-320.

First available in Project Euclid: 5 February 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q51: Soliton-like equations [See also 37K40] 37K35: Lie-Bäcklund and other transformations 7K45


Hoffman, A.; Wayne, C.E. Orbital stability of localized structures via Bäcklund transfomations. Differential Integral Equations 26 (2013), no. 3/4, 303--320. https://projecteuclid.org/euclid.die/1360092826

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