Complex solutions of Monge-Ampère equations
arXiv:1104.0362 · doi:10.1016/j.geomphys.2011.06.019
Abstract
We describe a method to reduce partial differential equations of Monge-Ampère type in 4 variables to complex partial differential equations in 2 variables. To illustrate this method, we construct explicit holomorphic solutions of the special lagrangian equation, the real Monge-Ampère equations and the Plebanski equations.
16 pages, 5 tables To appear in Journal of Geometry and Physics