KdV Surfaces

Details KdV Surfaces KdV Surfaces

2005-11-23

arxiv.org/abs/nlin/0511049v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

20 pages, Latex file

Scientific paper

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.

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