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