Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces
|
|
| Creator |
Gerdjikov, V.S.
Grahovski, G.G. Mikhailov, A.V. Valchev, T.I. |
|
| 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.
|
|
| Date |
2019-02-14T18:05:31Z
2019-02-14T18:05:31Z 2011 |
|
| Type |
Article
|
|
| Identifier |
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 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|