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General solutions of the Monge-Ampère equation in $n$-dimensional space

D. B. Fairlie·A. N. Leznov
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Abstract

It is shown that the general solution of a homogeneous Monge-Ampère equation in $n$-dimensional space is closely connected with the exactly (but only implicitly) integrable system \frac {\partial ξ_{j}}{\partial x_0}+\sum_{k=1}^{n-1} ξ_{k} \frac {\partial ξ_{j}}{\partial x_{k}}=0 \label{1} Using the explicit form of solution of this system it is possible to construct the general solution of the Monge-Ampère equation.

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D. B. Fairlie, A. N. Leznov. 1994-03-22. General solutions of the Monge-Ampère equation in $n$-dimensional space. https://doi.org/10.1016/0393-0440(94)00035-3

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