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math-ph2007★ 13 cited
Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics
A. A. Malykh, Y. Nutku, M. B. Sheftel
We demonstrate that partner symmetries provide a lift of noninvariant solutions of three-dimensional Boyer-Finley equation to noninvariant solutions of four-dimensional hyperbolic…
math-ph2004
Partner symmetries and non-invariant solutions of four-dimensional heavenly equations
A A Malykh, Y Nutku, M B Sheftel
We extend our method of partner symmetries to the hyperbolic complex Monge-Ampère equation and the second heavenly equation of Plebañski. We show the existence of partner symmetrie…
math-ph2003
Partner symmetries of the complex Monge-Ampere equation yield hyper-Kahler metrics without continuous symmetries
A. A. Malykh, Y. Nutku, M. B. Sheftel
We extend the Mason-Newman Lax pair for the elliptic complex Monge-Ampère equation so that this equation itself emerges as an algebraic consequence. We regard the function in the e…