Ernst equation

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

The Ernst equation[edit]

The equation reads:

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

Its usage[edit]

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