The cosh-Gordon equation is a nonlinear elliptic partial differential equation commonly normalized as
 |
Conventions in the literature may rescale the independent variables and the dependent variable, so
constant factors in front of 
and hyperbolic cosine
are not intrinsic.
The cosh-Gordon equation occurs as the Gauss part of the Gauss-Codazzi equations for surfaces of constant mean curvature in hyperbolic geometry. In particular, away from zeros of the Hopf differential, the Gauss part of the Gauss-Codazzi equations of a hyperbolic minimal surface can be reduced locally to a cosh-Gordon equation by a conformal change of coordinate and normalization of the Hopf differential (Bobenko 1991).
