Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 022, 14 pages      arXiv:1512.05817      https://doi.org/10.3842/SIGMA.2016.022

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

Błażej M. Szablikowski
Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland

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

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.

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

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