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.
Publié le : 2007-09-15
Classification:
Similarity geometry,
invariant geometric flow,
deformation of surface,
integrable system,
37K25,
53C44,
53A55
@article{1224877828,
author = {Qu, Changzheng and Li, Yanyan},
title = {Deformation of Surfaces Induced by Motions of Curves in Higherdimensional Similarity Geometries},
journal = {Methods Appl. Anal.},
volume = {14},
number = {1},
year = {2007},
pages = { 273-286},
language = {en},
url = {http://dml.mathdoc.fr/item/1224877828}
}
Qu, Changzheng; Li, Yanyan. Deformation of Surfaces Induced by Motions of Curves in Higherdimensional Similarity Geometries. Methods Appl. Anal., Tome 14 (2007) no. 1, pp. 273-286. http://gdmltest.u-ga.fr/item/1224877828/