Ernst equation

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

The Ernst equation

The equation reads:

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

Its usage

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


  1. Weisstein, Eric W, Ernst equation, MathWorld--A Wolfram Web.
  2. Biography of Frederick J. Ernst
  3. Harrison B.K. (1978), Backlund transformation for the Ernst equation of general relativity, Phys. Rev. Lett. 41, no. 18, 1197--1200.
  4. Marvan M. (2004), Recursion operators for vacuum Einstein equations with symmetries, in: Symmetry in nonlinear mathematical physics, Kyiv.arXiv:nlin/0401014
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