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The Lax-Sato approach to the hierarchies of Manakov-Santini type isformalized in order to extend it to a more general class of integrable systems.For this purpose some linear operators are introduced, which must satisfy someintegrability conditions, one of them is the Rota-Baxter identity. The theoryis illustrated by means of the algebra of Laurent series, the relatedhierarchies are classified and examples, also new, of Manakov-Santini typesystems are constructed, including those that are related to the dispersionlessmodified Kadomtsev-Petviashvili equation and so called dispersionless r-thsystems.

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