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      Korteweg-de Vries surfaces

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      Author(s)
      Gurses, M.
      Tek, S.
      Date
      2014-01
      Source Title
      Nonlinear Analysis: Theory, Methods and Applications
      Print ISSN
      0362-546X
      Publisher
      Elsevier
      Volume
      95
      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.
      Keywords
      Integrable Equations
      Shape Equation
      Soliton Surfaces
      Weingarten Surfaces
      Willmore Surfaces
      Permalink
      http://hdl.handle.net/11693/13348
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.na.2013.08.025
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