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

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

1994-10-03

arxiv.org/abs/solv-int/9409004v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

latex

Scientific paper

10.1088/0305-4470/27/23/026

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.

Affiliated with

Also associated with

No associations

Rating

On the Monge-Ampere equivalent of the sine-Gordon equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Monge-Ampere equivalent of the sine-Gordon equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Monge-Ampere equivalent of the sine-Gordon equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585594