In this paper, we study deformation of surfaces induced by adding one and two extra space variables to the motions of space curves in higher-dimensional similarity geometries. It is shown that the 2+1- and 3+1-dimensional nonlinear evolution equations including the 2+1-dimensional mKdV equation and a generalization to the mKdV-Burgers system arise from such motions.
Changzheng Qu. Yanyan Li. "Deformation of Surfaces Induced by Motions of Curves in Higherdimensional Similarity Geometries." Methods Appl. Anal. 14 (3) 273 - 286, September 2007.