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Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces
Інший ID:
2010 Mathematics Subject Classification: 37K20; 35Q51; 74J30; 78A60
DOI: http://dx.doi.org/10.3842/SIGMA.2011.096
DOI: http://dx.doi.org/10.3842/SIGMA.2011.096
Посилання:
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.
Підтримка:
This paper is a contribution to the Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria). The full collection is available at http://www.emis.de/journals/SIGMA/SIDE-9.html.
The authors have the pleasure to thank Professor Allan Fordy for numerous useful discussions. The authors acknowledge support from the Royal Society and the Bulgarian academy of sciences via joint research project “Reductions of Nonlinear Evolution Equations and analytic spectral theory”. The work of G.G.G. is supported by the Science Foundation of Ireland (SFI), under Grant no. 09/RFP/MTH2144. Finally we would like to thank one of the referees for useful suggestions.
Дата:
2011
Переглядів:
489
Завантажень:
223
Анотація:
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.
