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Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces

Gerdjikov, VS, Grahovski, GG, Mikhailov, AV and Valchev, TI (2011) Polynomial bundles and generalised Fourier transforms for integrable equations on A.III-type symmetric spaces. SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), 7. ISSN 1815-0659

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Abstract

A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes of soliton solutions associated with the Lax operator. Next, by using the Wronskian relations, the mapping between the potential and the minimal sets of scattering data is constructed. Furthermore, completeness relations for the 'squared solutions' (generalized exponentials) are derived. Next, expansions of the potential and its variation are obtained. This demonstrates that the interpretation of the inverse scattering method as a generalized Fourier transform holds true. Finally, the Hamiltonian structures of these generalized multi-component Heisenberg ferromagnetic (MHF) type integrable models on A.III-type symmetric spaces are briefly analyzed.

Item Type: Article
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 25 Oct 2011 08:20
Last Modified: 08 Feb 2013 17:34
Published Version: http://dx.doi.org/10.3842/SIGMA.2011.096
Status: Published
Publisher: National Academy of Science of Ukraine
Refereed: Yes
Identification Number: 10.3842/SIGMA.2011.096
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/43355

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