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.
References
- ↑ Weisstein, Eric W, Ernst equation, MathWorld--A Wolfram Web.
- ↑ Biography of Frederick J. Ernst
- ↑ Harrison B.K. (1978), Backlund transformation for the Ernst equation of general relativity, Phys. Rev. Lett. 41, no. 18, 1197--1200.
- ↑ 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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