Dispersionless Multi-Dimensional Integrable Systems and Related Conformal Structure Generating Equations of Mathematical Physics

Oksana Ye. Hentosh , Yarema A. Prykarpatskyy , Denis Blackmore , Anatolij K. Prykarpatsky

Abstract

Using diffeomorphism group vector fields on C-multiplied tori and the related Lie-algebraic structures, we study multi-dimensional dispersionless integrable systems that describe conformal structure generating equations of mathematical physics. An interesting modification of the devised Lie-algebraic approach subject to spatial-dimensional invariance and meromorphicity of the related differential-geometric structures is described and applied in proving complete integrability of some conformal structure generating equations. As examples, we analyze the Einstein-Weyl metric equation, the modified Einstein-Weyl metric equation, the Dunajski heavenly equation system, the first and second conformal structure generating equations and the inverse first Shabat reduction heavenly equation. We also analyze the modified Plebańnski heavenly equations, the Husain heavenly equation and the general Monge equation along with their multi-dimensional generalizations. In addition, we construct superconformal analogs of the Whitham heavenly equation.
Author Oksana Ye. Hentosh
Oksana Ye. Hentosh,,
-
, Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
, Denis Blackmore
Denis Blackmore,,
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, Anatolij K. Prykarpatsky
Anatolij K. Prykarpatsky,,
-
Journal seriesSymmetry Integrability and Geometry-Methods and Applications, [Symmetry, Integrability and Geometry - Methods and Applications], ISSN 1815-0659, (N/A 70 pkt)
Issue year2019
Vol15
Pages1-20
Publication size in sheets0.95
Article number079
Keywords in EnglishLax-Sato equations; multi-dimensional integrable heavenly equations; Lax integrability; Hamiltonian system; torus diffeomorphisms; loop Lie algebra; Lie-algebraic scheme; Casimir invariants; R-structure; Lie-Poisson structure; conformal structures; multidimensional heavenly equations
ASJC Classification2603 Analysis; 2608 Geometry and Topology; 2610 Mathematical Physics
DOIDOI:10.3842/SIGMA.2019.079
URL https://www.emis.de/journals/SIGMA/2019/079/sigma19-079.pdf
Internal identifierWIŚIG/2019/82
Languageen angielski
Score (nominal)70
Score sourcejournalList
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 0.647; WoS Impact Factor: 2018 = 1.088 (2) - 2018=0.984 (5)
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FinansowanieThanks are also due the Department of Physics, Mathematics and Computer Science of the Cracow University of Technology for a local research grant F-2/370/2018/DS. This work was partly funded by the budget program of Ukraine \Support for the development of priority research areas" (CPCEC 6451230).
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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