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

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creativework.keywordsIntegrals of motion, Reduction group, Riemann-Hilbert problem, Spectral decompositions
creativework.publisherInstitute of Mathematicsen
dc.contributor.authorGerdjikov V.S.
dc.contributor.authorGrahovski G.G.
dc.contributor.authorMikhailov A.V.
dc.contributor.authorValchev T.I.
dc.date.accessioned2024-07-10T14:27:03Z
dc.date.accessioned2024-07-10T14:48:08Z
dc.date.available2024-07-10T14:27:03Z
dc.date.available2024-07-10T14:48:08Z
dc.date.issued2011-01-01
dc.description.abstractA 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.
dc.identifier.doi10.3842/SIGMA.2011.096
dc.identifier.issn1815-0659
dc.identifier.scopusSCOPUS_ID:84930479227en
dc.identifier.urihttps://rlib.uctm.edu/handle/123456789/337
dc.language.isoen
dc.source.urihttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84930479227&origin=inward
dc.titlePolynomial bundles and Generalised Fourier transforms for integrable equations on A.III-type symmetric spaces
dc.typeArticle
oaire.citation.volume7
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