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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| Дата: | 2008 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-149036 |
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irk-123456789-1490362019-02-20T01:29:04Z Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type Gerdjikov, V.S. Kostov, N.A. 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. 2008 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149036 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 |
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. |
| format |
Article |
| author |
Gerdjikov, V.S. Kostov, N.A. |
| spellingShingle |
Gerdjikov, V.S. Kostov, N.A. Reductions of Multicomponent mKdV Equations on Symmetric Spaces of DIII-Type Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Gerdjikov, V.S. Kostov, N.A. |
| author_sort |
Gerdjikov, V.S. |
| title |
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_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_sort |
reductions of multicomponent mkdv equations on symmetric spaces of diii-type |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149036 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT gerdjikovvs reductionsofmulticomponentmkdvequationsonsymmetricspacesofdiiitype AT kostovna reductionsofmulticomponentmkdvequationsonsymmetricspacesofdiiitype |
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2023-05-20T17:32:02Z |
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2023-05-20T17:32:02Z |
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1796153513447784448 |