Special Isothermic Surfaces and Solitons

Details Special Isothermic Surfaces and Solitons Special Isothermic Surfaces and Solitons

2001-08-24

arxiv.org/abs/math/0108170v1

Contemp. Math. 288 (2001), 129-148

Mathematics

Differential Geometry

18 pages, 5 figures, to appear in the AMS Contemporary Mathematics Series, "Proceedings of the Congress in memory of Alfred Gr

Scientific paper

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.

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