This article is cited in 9 papers

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

Błazej M. Szablikowski

Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznán, Poland

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.

Keywords: Manakov–Santini hierarchy; Rota–Baxter identity; classical $r$-matrix formalism; generalized Lax hierarchies; integrable $(2+1)$-dimensional systems.

MSC: 37K10; 37K30

Received: January 11, 2016; in final form February 22, 2016; Published online February 27, 2016

Language: English

DOI: 10.3842/SIGMA.2016.022

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ArXiv: 1512.05817