Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with 4 × 4 ma...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2008 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148971 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions / A.G. Meshkov, M.Ju. Balakhnev // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 45 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862634808612487168 |
|---|---|
| author | Meshkov, A.G. Balakhnev, M.Ju. |
| author_facet | Meshkov, A.G. Balakhnev, M.Ju. |
| citation_txt | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions / A.G. Meshkov, M.Ju. Balakhnev // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 45 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with 4 × 4 matrices are presented.
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| first_indexed | 2025-11-30T16:38:06Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148971 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T16:38:06Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Meshkov, A.G. Balakhnev, M.Ju. 2019-02-19T12:15:45Z 2019-02-19T12:15:45Z 2008 Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions / A.G. Meshkov, M.Ju. Balakhnev // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 45 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 35Q53; 37K20 https://nasplib.isofts.kiev.ua/handle/123456789/148971 A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with 4 × 4 matrices are presented. We are grateful to Professor V.V. Sokolov for helpful discussions. This work was supported by Federal Agency for Education of Russian Federation, project # 1.5.07. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions Article published earlier |
| spellingShingle | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions Meshkov, A.G. Balakhnev, M.Ju. |
| title | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions |
| title_full | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions |
| title_fullStr | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions |
| title_full_unstemmed | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions |
| title_short | Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions |
| title_sort | two-field integrable evolutionary systems of the third order and their differential substitutions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148971 |
| work_keys_str_mv | AT meshkovag twofieldintegrableevolutionarysystemsofthethirdorderandtheirdifferentialsubstitutions AT balakhnevmju twofieldintegrableevolutionarysystemsofthethirdorderandtheirdifferentialsubstitutions |