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On a class of second-order PDEs admitting partner symmetries | | M. B. Sheftel
; A. A. Malykh
; | | Date: |
19 Apr 2009 | | Abstract: | Recently we have demonstrated how to use partner symmetries for obtaining
noninvariant solutions of heavenly equations of Plebanski that govern heavenly
gravitational metrics. In this paper, we present a class of scalar second-order
PDEs with four variables, that possess partner symmetries and contain only
second derivatives of the unknown. We present recursion relations for
symmetries for these PDEs. We also present a complete set of simplest canonical
forms to which the general PDE with partner symmetries can be transformed by
point and Legendre transformations, together with recursions for symmetries of
these canonical equations. These canonical forms contain the first and second
equations of Plebanski and also new equations which we call mixed heavenly
equation and asymmetric heavenly equation. On the example of the mixed heavenly
equation, we show how to use partner symmetries for obtaining noninvariant
solutions of PDEs by a lift from invariant solutions. | | Source: | arXiv, 0904.2909 | | Services: | Forum | Review | PDF | Favorites | |
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