特殊等温曲面和孤子

Special isothermic surfaces and soliton

给出了(A,0,C,D)型Darboux特殊等温曲面和二阶偏微分方程ΩΔΩ-Ω2+Ω4=s,s∈R解之间的对应,接着用等温曲面经典Darboux变换构造了这个方程的Ba¨cklund变换。作为应用,讨论了单孤子解和对应的曲面。

We establish a correspondence between Darboux,s special isothermic surfaces of type（A,0,C,D） and the solutions of the second order partial differential equation ΩΔΩ-｜Ω｜2＋Ω^4=s,s∈R.We then use the classical Darboux transformation for isothermic surfaces to construct a Backlund transformation for this equation.As an application,we discuss 1-soliton solutions and the corresponding surfaces.