On the Monge-Ampere equivalent of the sine-Gordon equation

E. V. Ferapontov; Y. Nutku

doi:10.1088/0305-4470/27/23/026

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On the Monge-Ampere equivalent of the sine-Gordon equation

E. V. Ferapontov·Y. Nutku

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Abstract

Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere equations.

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E. V. Ferapontov, Y. Nutku. 1994-10-03. On the Monge-Ampere equivalent of the sine-Gordon equation. https://doi.org/10.1088/0305-4470%2F27%2F23%2F026

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