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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 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.

preprint2016arXivOpen access
Blazej M. Szablikowski
math-phmath.MPnlin.SI
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Blazej M. Szablikowski

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