Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrictions on the jet order, the answer is given by a third order ordinary differential equation to govern the functional dependence of the principal curvatures. Employing the scaling and translation (offsetting) symmetry, we give a general solution of the governing equation in terms of elliptic integrals. We show that the instances when the elliptic integrals degenerate to elementary functions were known to nineteenth century geometers. Finally, we characterize the associated normal congruences.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation 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 Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of integrable Weingarten surfaces possessing an sl(2)-valued zero curvature representation will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-155005

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.