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The Lax–Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure

  • Oksana Hentosh
  • Yarema PrykarpatskyEmail author
Research Article
  • 5 Downloads

Abstract

A Lie-algebraic approach to constructing the Lax–Sato integrable superanalogs of heavenly equations by use of the loop Lie algebra of superconformal vector fields on a 1|N-dimensional supertorus is proposed. In the framework of this approach integrable superanalogs of the Mikhalev–Pavlov heavenly equation are obtained for all \(N\in {\mathbb {N}} {\setminus } \{ 4,5 \}\) as well as Shabat type reductions for all \(N\in {\mathbb {N}}\). The Lax–Sato integrable superanalogs of the generalized Liouville heavenly equations are found by means of the Lie algebra of holomorphic in “spectral” parameter superconformal vector fields on a 1|N-dimensional complex supertorus.

Keywords

Heavenly type equations Lax–Sato integrability Superconformal vector fields Adler–Kostant–Symes theory Casimir invariants 

Mathematics Subject Classification

37K05 37K30 37K65 35Q75 35Q35 17B80 58C50 

Notes

Acknowledgements

The authors cordially thank Prof. Maciej Błaszak, Prof. Błażej Szablikowski and Prof. Jan Cieśliński for fruitful discussions during the International Conference in Functional Analysis dedicated to the 125th anniversary of Stefan Banach held on September 18–23, 2017, in Lviv, Ukraine.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, The NAS of UkraineLvivUkraine
  2. 2.Department of Applied MathematicsUniversity of Agriculture in KrakówKrakówPoland

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