Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type
New reductions for the multicomponent modified Korteweg-de Vries (MMKdV) equations on the symmetric spaces of DIII-type are derived using the approach based on the reduction group introduced by A.V. Mikhailov. The relevant inverse scattering problem is studied and reduced to a Riemann-Hilbert proble...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2008 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149036 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type / V.S. Gerdjikov, N.A. Kostov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862621209462571008 |
|---|---|
| author | Gerdjikov, V.S. Kostov, N.A. |
| author_facet | Gerdjikov, V.S. Kostov, N.A. |
| citation_txt | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type / V.S. Gerdjikov, N.A. Kostov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | New reductions for the multicomponent modified Korteweg-de Vries (MMKdV) equations on the symmetric spaces of DIII-type are derived using the approach based on the reduction group introduced by A.V. Mikhailov. The relevant inverse scattering problem is studied and reduced to a Riemann-Hilbert problem. The minimal sets of scattering data Ti, i = 1, 2 which allow one to reconstruct uniquely both the scattering matrix and the potential of the Lax operator are defined. The effect of the new reductions on the hierarchy of Hamiltonian structures of MMKdV and on Ti are studied. We illustrate our results by the MMKdV equations related to the algebra g @ so(8) and derive several new MMKdV-type equations using group of reductions isomorphic to Z₂, Z₃, Z₄.
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| first_indexed | 2025-12-07T13:23:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149036 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:23:57Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Gerdjikov, V.S. Kostov, N.A. 2019-02-19T13:11:32Z 2019-02-19T13:11:32Z 2008 Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type / V.S. Gerdjikov, N.A. Kostov // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 30 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K20; 35Q51; 74J30; 78A60 https://nasplib.isofts.kiev.ua/handle/123456789/149036 New reductions for the multicomponent modified Korteweg-de Vries (MMKdV) equations on the symmetric spaces of DIII-type are derived using the approach based on the reduction group introduced by A.V. Mikhailov. The relevant inverse scattering problem is studied and reduced to a Riemann-Hilbert problem. The minimal sets of scattering data Ti, i = 1, 2 which allow one to reconstruct uniquely both the scattering matrix and the potential of the Lax operator are defined. The effect of the new reductions on the hierarchy of Hamiltonian structures of MMKdV and on Ti are studied. We illustrate our results by the MMKdV equations related to the algebra g @ so(8) and derive several new MMKdV-type equations using group of reductions isomorphic to Z₂, Z₃, Z₄. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). It is our pleasure to thank Professor Gaetano Vilasi for useful discussions. One of us (VSG) thanks the Physics Department of the University of Salerno for the kind hospitality and the Italian Istituto Nazionale di Fisica Nucleare for financial support. We also thank the Bulgarian Science Foundation for partial support through contract No. F-1410. One of us (VSG) is grateful to the organizers of the Kyiv conference for their hospitality and acknowledges financial support by an CEI grant. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type Article published earlier |
| spellingShingle | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type Gerdjikov, V.S. Kostov, N.A. |
| title | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type |
| title_full | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type |
| title_fullStr | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type |
| title_full_unstemmed | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type |
| title_short | Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type |
| title_sort | reductions of multicomponent mkdv equations on symmetric spaces of diii-type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149036 |
| work_keys_str_mv | AT gerdjikovvs reductionsofmulticomponentmkdvequationsonsymmetricspacesofdiiitype AT kostovna reductionsofmulticomponentmkdvequationsonsymmetricspacesofdiiitype |