sinh-Gordon方程单周期解的一个spectral theory
A spectral theory for simply periodic solutions of the sinh-Gordon equation
摘要：
在这项工作中，频谱理论的2维，简单的周期，复值解决方案u的sinh-Gordon方程的发展。光谱数据，这样的解决方案的定义（以下希钦和Bobenko）和空间的光谱数据所描述的渐近表征。使用渐近估计的方法，谱数据的逆问题沿着一条线求解，即，解u在一条线上从谱数据重建。最后构造了谱曲线的Jacobi簇和Abel映射，用来描述解u平移时谱数据的变化。
英文摘要：
In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally a Jacobi variety and Abel map for the spectral curve is constructed; they are used to describe the change of the spectral data under translation of the solution u.
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