  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.
