General solutions of the Monge-Amp\`{e}re equation in $n$-dimensional space
High Energy Physics - Theory
2016-09-06 v1 Analysis of PDEs
Exactly Solvable and Integrable Systems
solv-int
Abstract
It is shown that the general solution of a homogeneous Monge-Amp\`{e}re equation in -dimensional space is closely connected with the exactly (but only implicitly) integrable system \frac {\partial \xi_{j}}{\partial x_0}+\sum_{k=1}^{n-1} \xi_{k} \frac {\partial \xi_{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-Amp\`{e}re equation.
Cite
@article{arxiv.hep-th/9403134,
title = {General solutions of the Monge-Amp\`{e}re equation in $n$-dimensional space},
author = {D. B. Fairlie and A. N. Leznov},
journal= {arXiv preprint arXiv:hep-th/9403134},
year = {2016}
}
Comments
8 pages