On some exact solutions of heavenly equations in four dimensions | Zendy

Łukasz T. Stȩpień | Zendy

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On some exact solutions of heavenly equations in four dimensions

Author(s) -

Łukasz T. Stȩpień

Publication year - 2020

Publication title -

aip advances

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.421

H-Index - 58

ISSN - 2158-3226

DOI - 10.1063/1.5144327

Subject(s) - invariant (physics) , mathematics , hyperbolic partial differential equation , pure mathematics , mathematical analysis , mathematical physics , differential equation

Some new classes of exact solutions (so-called functionally-invariant solutions) of the elliptic and hyperbolic complex Monge-Amp$\grave{e}$re equations and of the second heavenly equation, mixed heavenly equation, asymmetric heavenly equation, evolution form of second heavenly equation, general heavenly equation, real general heavenly equation and one of the real sections of general heavenly equation, are found. Besides non-invariance of these found classes of solutions has been investigated. These classes of solutions determine the new classes of metrics without Killing vectors. A criterion of non-invariance of the solutions belonging to found classes, has been also formulated.

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