Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability conditions, one of them is the Rota-Baxter identity. The th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147416 |
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| Cite this: | Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities / B.M Szablikowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 34 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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Szablikowski, B.M. 2019-02-14T18:09:26Z 2019-02-14T18:09:26Z 2016 Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities / B.M Szablikowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 34 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 37K30 DOI:10.3842/SIGMA.2016.022 https://nasplib.isofts.kiev.ua/handle/123456789/147416 The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability conditions, one of them is the Rota-Baxter identity. The theory is illustrated by means of the algebra of Laurent series, the related hierarchies are classified and examples, also new, of Manakov-Santini type systems are constructed, including those that are related to the dispersionless modified Kadomtsev-Petviashvili equation and so called dispersionless r-th systems. The very preliminary results related to this work were obtained in 2010 during the visit of the author to Institute of Mathematics in Academia Sinica in Taipei. The author wishes to express his thanks to Professor Jen-Hsu Chang for valuable discussions and Professor Jyh-Hao Lee for warm hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities |
| spellingShingle |
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities Szablikowski, B.M. |
| title_short |
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities |
| title_full |
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities |
| title_fullStr |
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities |
| title_full_unstemmed |
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities |
| title_sort |
hierarchies of manakov-santini type by means of rota-baxter and other identities |
| author |
Szablikowski, B.M. |
| author_facet |
Szablikowski, B.M. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The Lax-Sato approach to the hierarchies of Manakov-Santini type is formalized in order to extend it to a more general class of integrable systems. For this purpose some linear operators are introduced, which must satisfy some integrability conditions, one of them is the Rota-Baxter identity. The theory is illustrated by means of the algebra of Laurent series, the related hierarchies are classified and examples, also new, of Manakov-Santini type systems are constructed, including those that are related to the dispersionless modified Kadomtsev-Petviashvili equation and so called dispersionless r-th systems.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147416 |
| citation_txt |
Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities / B.M Szablikowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 34 назв. — англ. |
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AT szablikowskibm hierarchiesofmanakovsantinitypebymeansofrotabaxterandotheridentities |
| first_indexed |
2025-12-07T16:21:11Z |
| last_indexed |
2025-12-07T16:21:11Z |
| _version_ |
1850867157951315968 |