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Partner symmetries and non-invariant solutions of four-dimensional heavenly equations | | A A Malykh
; Y Nutku
; M B Sheftel
; | | Date: |
12 Mar 2004 | | Journal: | J.Phys. A37 (2004) 7527-7546 | | Subject: | Mathematical Physics; Differential Geometry MSC-class: 35Q75; 83C15 | math-ph gr-qc math.DG math.MP | | Abstract: | We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Pleba~nski. We show the existence of partner symmetries and derive the relations between them for both equations. For certain simple choices of partner symmetries the resulting differential constraints together with the original heavenly equations are transformed to systems of linear equations by an appropriate Legendre transformation. The solutions of these linear equations are generically non-invariant. As a consequence we obtain explicitly new classes of heavenly metrics without Killing vectors. | | Source: | arXiv, math-ph/0403020 | | Services: | Forum | Review | PDF | Favorites | |
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