论文标题
一阶线性系统的反向散射问题中的广义Marchenko方法
The generalized Marchenko method in the inverse scattering problem for a first-order linear system
论文作者
论文摘要
Marchenko方法是在反向散射问题中开发的，该线性系统的一阶微分方程的线性系统包含与光谱参数成正比的电势。积分方程的相应Marchenko系统以某种方式得出，该方法可以应用于尚不可用的其他线性系统。它显示了如何从Marchenko系统的解决方案构建线性系统的电势和散射解决方案。线性系统的结合状态信息具有任意数量的绑定状态和任何多重性，用一对恒定矩阵三重态描述。当线性系统中的电势无反射时，以封闭形式出现了一些显式溶液公式，以提供线性系统的电势和散射解决方案。该理论用一些明确的例子进行了说明。
The Marchenko method is developed in the inverse scattering problem for a linear system of first-order differential equations containing potentials proportional to the spectral parameter. The corresponding Marchenko system of integral equations is derived in such a way that the method can be applied to some other linear systems for which a Marchenko method is not yet available. It is shown how the potentials and the scattering solutions to the linear system are constructed from the solution to the Marchenko system. The bound-state information for the linear system with any number of bound states and any multiplicities is described in terms of a pair of constant matrix triplets. When the potentials in the linear system are reflectionless, some explicit solution formulas are presented in closed form for the potentials and for the scattering solutions to the linear system. The theory is illustrated with some explicit examples.
