English

KdV Surfaces

Exactly Solvable and Integrable Systems 2007-05-23 v1 General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Differential Geometry math.MP

Abstract

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

Keywords

Cite

@article{arxiv.nlin/0511049,
  title  = {KdV Surfaces},
  author = {Metin Gurses and Suleyman Tek},
  journal= {arXiv preprint arXiv:nlin/0511049},
  year   = {2007}
}

Comments

20 pages, Latex file