Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures
We show that evolutionary Hirota-type Euler-Lagrange equations in (2+1) dimensions have a symplectic Monge-Ampère form. We consider integrable equations of this type in the sense that they admit infinitely many hydrodynamic reductions and determine Lax pairs for them. For two seven-parameter familie...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209447 |
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| Cite this: | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures / M.B. Sheftel, D. Yazici // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862747567720235008 |
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| author | Sheftel, M.B. Yazici, D. |
| author_facet | Sheftel, M.B. Yazici, D. |
| citation_txt | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures / M.B. Sheftel, D. Yazici // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that evolutionary Hirota-type Euler-Lagrange equations in (2+1) dimensions have a symplectic Monge-Ampère form. We consider integrable equations of this type in the sense that they admit infinitely many hydrodynamic reductions and determine Lax pairs for them. For two seven-parameter families of integrable equations converted to two-component form, we have constructed Lagrangians, recursion operators, and bi-Hamiltonian representations. We have also presented a six-parameter family of tri-Hamiltonian systems.
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| first_indexed | 2025-12-07T20:51:44Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209447 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:51:44Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sheftel, M.B. Yazici, D. 2025-11-21T19:00:43Z 2018 Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures / M.B. Sheftel, D. Yazici // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 18 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q75; 37K05; 37K10 arXiv: 1712.01549 https://nasplib.isofts.kiev.ua/handle/123456789/209447 https://doi.org/10.3842/SIGMA.2018.017 We show that evolutionary Hirota-type Euler-Lagrange equations in (2+1) dimensions have a symplectic Monge-Ampère form. We consider integrable equations of this type in the sense that they admit infinitely many hydrodynamic reductions and determine Lax pairs for them. For two seven-parameter families of integrable equations converted to two-component form, we have constructed Lagrangians, recursion operators, and bi-Hamiltonian representations. We have also presented a six-parameter family of tri-Hamiltonian systems. The authors are grateful to an anonymous referee for important remarks that contributed to the improvement of our paper. The research of M.B. Sheftel is partly supported by the research grant from Boğaziçi University Scientific Research Fund (BAP), research project No. 11643. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures Article published earlier |
| spellingShingle | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures Sheftel, M.B. Yazici, D. |
| title | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures |
| title_full | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures |
| title_fullStr | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures |
| title_full_unstemmed | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures |
| title_short | Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures |
| title_sort | evolutionary hirota type (2+1)-dimensional equations: lax pairs, recursion operators and bi-hamiltonian structures |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209447 |
| work_keys_str_mv | AT sheftelmb evolutionaryhirotatype21dimensionalequationslaxpairsrecursionoperatorsandbihamiltonianstructures AT yazicid evolutionaryhirotatype21dimensionalequationslaxpairsrecursionoperatorsandbihamiltonianstructures |