三次非线性薛定谔方程的Atiyah-Hitchin解I.一般电位
The Atiyah-Hitchin Bracket for the Cubic Nonlinear Schrodinger Equation. I. General Potentials
摘要：
这是第一次在一系列文件的泊松形式主义的三次非线性薛定谔方程排斥非线性及其关系复杂的几何形状。本文研究一般连续势。我们证明了相应的辅助Dirac谱问题的Weyl函数进行自然的泊松结构。我们称之为阿蒂亚-希钦泊松括号。我们证明了相空间上的Poisson括号是Weyl函数上的Atiyah-Hitchin括号在逆谱变换下的图像。
英文摘要：
This is the first in a series of papers on Poisson formalism for the cubic nonlinear Schrödinger equation with repulsive nonlinearity and its relation to complex geometry. In this paper we study general continuous potentials. We demonstrate that the Weyl functions of the corresponding auxiliary Dirac spectral problem carry a natural Poisson structure. We call it the Atiyah--Hitchin Poisson bracket. We show that the Poisson bracket on the phase space is the image of the Atiyah--Hitchin bracket on Weyl functions under the inverse spectral transform.
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