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On equations which describe pseudospherical surfaces. (English) Zbl 0696.35111

A characterization of the equations of the type \[ u_{xt}=F(u,u_ x,...,\partial^ ku/\partial x^ k),\quad k\geq 2, \] describing \(\eta\)- pseudospherical surfaces is obtained and applied to some special equations which are thus “discovered” as describing such surfaces.
Reviewer: V.Răsvan

MSC:

35L70 Second-order nonlinear hyperbolic equations
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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