Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics
Document Type
Article
Publication Date
1-1-2019
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 Plebański 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.
Identifier
85074107922 (Scopus)
Publication Title
Symmetry Integrability and Geometry Methods and Applications Sigma
External Full Text Location
https://doi.org/10.3842/SIGMA.2019.079
e-ISSN
18150659
Volume
15
Grant
CPCEC 6451230
Fund Ref
Politechnika Krakowska
Recommended Citation
Hentosh, Oksana Ye; Prykarpatsky, Yarema A.; Blackmore, Denis; and Prykarpatski, Anatolij K., "Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics" (2019). Faculty Publications. 8105.
https://digitalcommons.njit.edu/fac_pubs/8105