Modified Korteweg-de Vries surfaces

In this work, we consider 2-surfaces in R-3 arising from the modified Korteweg-de Vries (mKdV) equation. We give a method for constructing the position vector of the mKdV surface explicitly for a given solution of the mKdV equation. mKdV surfaces contain Willmore-like and Weingarten surfaces. We show that some mKdV surfaces can be obtained from a variational principle where the Lagrange function is a polynomial of the Gaussian and mean curvatures. (c) 2007 American Institute of Physics.