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

[摘要] 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.

[关键词] Manakov–Santini hierarchy;Rota–Baxter identity;classical r-matrix formalism;generalized Lax hierarchies;integrable (2 + 1)-dimensional systems