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

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.

8 pages

References in corpus (4)

• Universal Field Equations with Covariant Solutions D.B. Fairlie
• Euler Hierarchies and Universal Equations
• Linearisation of Universal Field Equations
• Equations of Hydrodynamic Type

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