Ernst equation

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

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.

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

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