谱方法用于半经典反聚焦戴维斯托尔二阶方程的散射图
Spectral approach to the scattering map for the semi-classical defocusing Davey-Stewartson II equation
AI总结：
本文提出了一种数值方法，用于解决半经典D-bar问题，通过将D-bar问题转化为复线性二次积分方程，并利用离散傅里叶变换和解析计算进行正则化，从而求解得到代数方程。
摘要：
反聚焦戴维斯托尔二阶方程的反散射方法由一组D-bar方程给出。我们提出了一种数值方法，用于处理实分析快速递减势的半经典D-bar问题。我们将D-bar问题视为一个复线性二次积分方程，该方程通过离散傅里叶变换与对奇异部分的显式解析计算相结合进行求解。所得到的代数方程通过固定点迭代或GMRES方法求解。讨论了系统中半经典参数小值情况下的几个例子。
英文摘要：
The inverse scattering approach for the defocusing Davey-Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We treat the D-bar problem as a complex linear second order integral equation which is solved with discrete Fourier transforms complemented by a regularization of the singular parts by explicit analytic computation. The resulting algebraic equation is solved either by fixed point iterations or GMRES. Several examples for small values of the semi-classical parameter in the system are discussed.
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