Special Isothermic Surfaces and Solitons
微分几何
2007-12-06 v1
摘要
We establish a correspondence between Darboux's special isothermic surfaces of type (A,0,C,D) and the solutions of the second order PDE : u\Delta(u)-|\nabla(u)|^{2}+\Phi^{4}=s, s \in R. We then use the classical Darboux transformation for isothermic surfaces to construct a B\"acklund transformation for this equation and prove a superposition formula for its solutions. As an application we discuss 1 and 2-soliton solutions and the corresponding surfaces.
引用
@article{arxiv.math/0108170,
title = {Special Isothermic Surfaces and Solitons},
author = {Emilio Musso and Lorenzo Nicolodi},
journal= {arXiv preprint arXiv:math/0108170},
year = {2007}
}
备注
18 pages, 5 figures, to appear in the AMS Contemporary Mathematics Series, "Proceedings of the Congress in memory of Alfred Gray" (eds. M. Fernandez, J.A. Wolf)