Korteweg-de Vries surfaces

Date

2014-01

Authors

Gurses, M.
Tek, S.

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Abstract

We consider 2-surfaces arising from the Korteweg-de Vries (KdV) hierarchy and the KdV equation. The surfaces corresponding to the KdV equation are in a three-dimensional Minkowski (M3) space. They contain a family of quadratic Weingarten and Willmore-like surfaces. We show that some KdV surfaces can be obtained from a variational principle where the Lagrange function is a polynomial function of the Gaussian and mean curvatures. We also give a method for constructing the surfaces explicitly, i.e., finding their parameterizations or finding their position vectors.© 2013 Elsevier Ltd. All rights reser.

Source Title

Nonlinear Analysis: Theory, Methods and Applications

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Elsevier

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Published Version (Please cite this version)

Language

English