Ernst equation

In mathematics, the Ernst equation^[1] is an integrable non-linear partial differential equation, named after the American physicist  [Wikidata].^[2]

The Ernst equation[]

The equation reads:

$${\displaystyle \Re (u)(u_{rr}+u_{r}/r+u_{zz})=(u_{r})^{2}+(u_{z})^{2}.}$$

For its Lax pair and other features see e.g. ^[3][4] and references therein.

Usage[]

The Ernst equation is employed in order to produce the exact solutions of the Einstein's equations in the general theory of relativity.

References[]