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Special Isothermic Surfaces and Solitons

Emilio Musso·Lorenzo Nicolodi
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Abstract

We establish a correspondence between Darboux's special isothermic surfaces of type (A,0,C,D) and the solutions of the second order PDE : uΔ(u)-|\nabla(u)|^{2}+Φ^{4}=s, s \in R. We then use the classical Darboux transformation for isothermic surfaces to construct a Bäcklund 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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Emilio Musso, Lorenzo Nicolodi. 2001-08-24. Special Isothermic Surfaces and Solitons. https://arxiv.org/abs/math/0108170

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