Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces
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,...
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| Дата: | 2011 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147414 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces / V.S. Gerdjikov, G.G. Grahovski, A.V. Mikhailov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 51 назв. — англ. |
Репозитарії
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irk-123456789-1474142019-02-15T01:23:52Z Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces Gerdjikov, V.S. Grahovski, G.G. Mikhailov, A.V. Valchev, T.I. 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. 2011 Article Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces / V.S. Gerdjikov, G.G. Grahovski, A.V. Mikhailov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 51 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K20; 35Q51; 74J30; 78A60 DOI: http://dx.doi.org/10.3842/SIGMA.2011.096 http://dspace.nbuv.gov.ua/handle/123456789/147414 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Gerdjikov, V.S. Grahovski, G.G. Mikhailov, A.V. Valchev, T.I. |
| spellingShingle |
Gerdjikov, V.S. Grahovski, G.G. Mikhailov, A.V. Valchev, T.I. Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Gerdjikov, V.S. Grahovski, G.G. Mikhailov, A.V. Valchev, T.I. |
| author_sort |
Gerdjikov, V.S. |
| title |
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces |
| title_short |
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces |
| title_full |
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces |
| title_fullStr |
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces |
| title_full_unstemmed |
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces |
| title_sort |
polynomial bundles and generalised fourier transforms for integrable equations on a.iii-type symmetric spaces |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147414 |
| citation_txt |
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces / V.S. Gerdjikov, G.G. Grahovski, A.V. Mikhailov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 51 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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