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The connection of Monge-Bateman equations with ordinary differential equations and their generalisation

A. N. Leznov
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Abstract

It is shown that the Monge equation is equivalent to the ordinary differential equation $\ddot X=0$ of free motion. Equations of Monge type (with their general solutions) are connected with each ordinary differential equation of second order $\ddot X=F(\dot X,X; t)$, integrable by quadratures. The result is generalised to a system of equations of the second order, which is in one to one correspondence with the multidimensional Monge-Bateman system.

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A. N. Leznov. 1999-08-10. The connection of Monge-Bateman equations with ordinary differential equations and their generalisation. https://arxiv.org/abs/math-ph/9908013

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