Korteweg-de Vries surfaces
Date
2014-01
Authors
Gurses, M.
Tek, S.
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Source Title
Nonlinear Analysis: Theory, Methods and Applications
Print ISSN
0362-546X
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Publisher
Elsevier
Volume
95
Issue
Pages
11 - 22
Language
English
Type
Article
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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.
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Keywords
Integrable Equations, Shape Equation, Soliton Surfaces, Weingarten Surfaces, Willmore Surfaces