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...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2016
Main Author: Szablikowski, B.M.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147416
Tags: Add Tag
No Tags, Be the first to tag this record!
Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147416
record_format dspace
spelling 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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
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.
work_keys_str_mv AT szablikowskibm hierarchiesofmanakovsantinitypebymeansofrotabaxterandotheridentities
first_indexed 2025-12-07T16:21:11Z
last_indexed 2025-12-07T16:21:11Z
_version_ 1850867157951315968