Tek, S.2015-07-282015-07-2820070022-2488http://hdl.handle.net/11693/11604In this work, we consider 2-surfaces in R3 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. © 2007 American Institute of Physics.EnglishSoliton SurfacesLie-algebrasGeometryArticle10.1063/1.2409523