The partial differential equation
+(u_r)/r+u_(zz))=u_r^2+u_z^2,](/images/equations/ErnstEquation/NumberedEquation1.svg) |
where ![R[u]](/images/equations/ErnstEquation/Inline1.svg)
is the real part of 
(Calogero and Degasperis 1982, p. 62; Zwillinger 1997,
p. 131).
Ernst Equation
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References
Calogero, F. and Degasperis, A. Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations. New York: North-Holland, 1982.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 131, 1997.Referenced on Wolfram|Alpha
Ernst EquationCite this as:
Weisstein, Eric W. "Ernst Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ErnstEquation.html