Special Isothermic Surfaces and Solitons
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 : u(u)-|∇(u)|2+4=s, s ∈ 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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