On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation
Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle θ are constructed and then reduced to the two-component Camassa-Holm model. Only three different independent classes of reductions are encountered corresponding to the angle θ being 0, π/2 or taking any value i...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146097 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation / H. Aratyn, J.F. Gomes, A.H. Zimerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862597189830705152 |
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| author | Aratyn, H. Gomes, J.F. Zimerman, A.H. |
| author_facet | Aratyn, H. Gomes, J.F. Zimerman, A.H. |
| citation_txt | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation / H. Aratyn, J.F. Gomes, A.H. Zimerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle θ are constructed and then reduced to the two-component Camassa-Holm model. Only three different independent classes of reductions are encountered corresponding to the angle θ being 0, π/2 or taking any value in the interval 0 < θ < π/2. This construction induces Bäcklund transformations between solutions of the two-component Camassa-Holm model associated with different classes of reduction.
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| first_indexed | 2025-11-27T17:05:46Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146097 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T17:05:46Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Aratyn, H. Gomes, J.F. Zimerman, A.H. 2019-02-07T13:11:01Z 2019-02-07T13:11:01Z 2006 On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation / H. Aratyn, J.F. Gomes, A.H. Zimerman // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 21 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 35Q53; 53A07; 53B50 https://nasplib.isofts.kiev.ua/handle/123456789/146097 Different gauge copies of the Ablowitz-Kaup-Newell-Segur (AKNS) model labeled by an angle θ are constructed and then reduced to the two-component Camassa-Holm model. Only three different independent classes of reductions are encountered corresponding to the angle θ being 0, π/2 or taking any value in the interval 0 < θ < π/2. This construction induces Bäcklund transformations between solutions of the two-component Camassa-Holm model associated with different classes of reduction. This paper is a contribution to the Proceedings of the O’Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 22–24, 2006, Budapest, Hungary). H.A. acknowledges partial support from Fapesp and IFT-UNESP for their hospitality. JFG and AHZ thank CNPq for a partial support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation Article published earlier |
| spellingShingle | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation Aratyn, H. Gomes, J.F. Zimerman, A.H. |
| title | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation |
| title_full | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation |
| title_fullStr | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation |
| title_full_unstemmed | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation |
| title_short | On a Negative Flow of the AKNS Hierarchy and Its Relation to a Two-Component Camassa-Holm Equation |
| title_sort | on a negative flow of the akns hierarchy and its relation to a two-component camassa-holm equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146097 |
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