Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities

Abstract

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.

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Cited by in corpus (3)

• The integrable heavenly type equations and their Lie-algebraic structure
• Dispersionless (3+1)-dimensional integrable hierarchies
• Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics