mKdV Surfaces
arXiv:math-ph/0612076 · doi:10.1063/1.2409523
Abstract
In this work, we consider 2-surfaces in 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.
24 pages