标题： 可积的导数非线性薛定谔方程系统的逆散射方法 显示英文标题

标题： Inverse scattering method for an integrable system of derivative nonlinear Schrödinger equations

摘要： 我们提出一种解法，用于可积系统（导数非线性薛定谔II系统）或陈-李-刘系统。 这是通过为相应的具有能量依赖势的常微分方程线性系统的逆散射问题提供一种解法技术来实现的。 相关的逆散射问题是通过建立一个线性积分方程组来解决的，我们将其称为马尔琴科线性积分方程组。 在求解逆散射问题时，我们使用包含传输系数、反射系数以及以一对矩阵三元组形式呈现的束缚态信息的输入数据集。 将我们的数据集作为马尔琴科方程组的输入，我们从马尔琴科方程组的解中恢复势函数。 通过使用时间演化的输入数据集，我们恢复时间演化的势函数，这些势函数构成可积DNLS II系统的解。 显示英文摘要

摘要： We present a solution method for the integrable system (derivative nonlinear Schr\"odinger II system) or the Chen--Lee--Liu system. This is done by presenting a solution technique for the inverse scattering problem for the corresponding linear system of ordinary differential equations with energy-dependent potentials. The relevant inverse scattering problem is solved by establishing a system of linear integral equations, which we refer to as the Marchenko system of linear integral equations. In solving the inverse scattering problem we use the input data set consisting of a transmission coefficient, a reflection coefficient, and the bound-state information presented in the form of a pair of matrix triplets. Using our data set as input to the Marchenko system, we recover the potentials from the solution to the Marchenko system. By using the time-evolved input data set, we recover the time-evolved potentials, where those potentials form a solution to the integrable DNLS II system.