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Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
Інший ID:
2010 Mathematics Subject Classification: 37K10; 37K30
DOI:10.3842/SIGMA.2016.022
DOI:10.3842/SIGMA.2016.022
Посилання:
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.
Підтримка:
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.
Дата:
2016
Переглядів:
572
Завантажень:
236
Анотація:
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.
