论文标题
Zakharov-Shabat系统的左右逆散射问题配方
Right and left inverse scattering problems formulations for the Zakharov-Shabat system
论文作者
论文摘要
我们考虑Zakharov-Shabat系统的反向散射问题的左右公式以及相应的整体Gelfand-Levitan-Marchenko方程。这两种公式都有助于对反散射问题的数值求解，我们使用先前开发的Toeplitz内边界（TIB）算法执行。首先，我们在左右散射系数之间建立了一般关系。在这里，除了已知的结果外，我们还引入了N-Soliton溶液的左右标准系数之间的关系。然后，我们提出了左Gelfand-Levitan-Marchenko方程的辅助内核，该方程允许一个人以数字方式解决右散射问题。我们将最初在左公式中提出的TIB算法推广到带有所获得的公式的右散射问题案例。 TIB算法的测试运行说明了我们的结果，从其正确的散射数据中重建了各种非对称电位。
We consider right and left formulations of the inverse scattering problem for the Zakharov-Shabat system and the corresponding integral Gelfand-Levitan-Marchenko equations. Both formulations are helpful for numerical solving of the inverse scattering problem, which we perform using the previously developed Toeplitz Inner Bordering (TIB) algorithm. First, we establish general relations between the right and left scattering coefficients. Here, along with the known results, we introduce a relation between the left and right norming coefficients for the N-soliton solution. Then we propose an auxiliary kernel of the left Gelfand-Levitan-Marchenko equations, which allows one to solve the right scattering problem numerically. We generalize the TIB algorithm, initially proposed in the left formulation, to the right scattering problem case with the obtained formulas. The test runs of the TIB algorithm illustrate our results reconstructing the various nonsymmetrical potentials from their right scattering data.
