Geodesic
Hierarchies of Manakov–Santini Type by Means of Rota–Baxter and Other Identities
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Manakov–Santini hierarchy; Rota–Baxter identity; classical $r$-matrix formalism; generalized Lax hierarchies; integrable $(2+1)$-dimensional systems. 
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     title = {Hierarchies of {Manakov{\textendash}Santini} {Type} by {Means} of {Rota{\textendash}Baxter} and {Other} {Identities}},
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}
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Błazej M. Szablikowski. Hierarchies of Manakov–Santini Type by Means of Rota–Baxter and Other Identities. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a21/

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