The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure

Hentosh, O.E., Prykarpatsky, Y.A., Balinsky, Alexander ORCID: https://orcid.org/0000-0002-8151-4462 and Prykarpatski, A.K. 2019. The dispersionless completely integrable heavenly type Hamiltonian flows and their differential-geometric structure. Annals of Mathematics and Physics 2 (1) , 011-025. 10.17352/amp.000006

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Abstract

There are reviewed modern investigations devoted to studying nonlinear dispersiveless heavenly type integrable evolutions systems on functional spaces within the modern differential-geometric and algebraic tools. Main accent is done on the loop diffeomorphism group vector fi elds on the complexifi ed torus and the related Lie-algebraic structures, generating dispersionless heavenly type integrable systems. As examples, we analyzed the Einstein–Weyl metric equation, the modifi ed Einstein–Weyl metric equation, the Dunajski heavenly equation system, the fi rst and second conformal structure generating equations, the inverse fi rst Shabat reduction heavenly equation, the fi rst and modifi ed Plebański heavenly equations, the Husain heavenly equation, the general Monge equation and the classical Korteweg-de Vries dispersive dynamical system. We also investigated geometric structures of a class of spatially one-dimensional completely integrable Chaplygin type hydrodynamic systems, which proved to be deeply connected with differential systems on the complexifi ed torus and the related diffeomorphism group orbits on them

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Date of First Compliant Deposit:	17 December 2019
Date of Acceptance:	27 August 2019
Last Modified:	05 May 2023 03:54
URI:	https://orca.cardiff.ac.uk/id/eprint/127599

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