论文标题
Marchenko方法解决了衍生化非线性Schrödinger方程的一般系统
The Marchenko method to solve the general system of derivative nonlinear Schrödinger equations
论文作者
论文摘要
提出了线性积分方程的系统，这是Marchenko积分方程系统的类似物，以解决与衍生NLS方程相关的线性系统的反散射问题。分析了相应的直接散射问题和反向散射问题，并描述了从解决方案到Marchenko系统的电势的恢复和JOST解决方案的恢复。当反射系数为零时，根据一对恒定矩阵三重态为电势和jost解提供了一些明确的解公式，这些固定矩阵三重态代表任何数量的绑定状态和任何多重性。在减少的情况下，当线性系统中的两个电势通过复杂的共轭相互关联时，获得相应的降低的Marchenko积分方程。从降低的Marchenko积分方程的溶液中获得了衍生NLS方程的解。提出的理论用一些明确的例子进行了说明。
A system of linear integral equations is presented, which is the analog of the system of Marchenko integral equations, to solve the inverse scattering problem for the linear system associated with the derivative NLS equations. The corresponding direct and inverse scattering problems are analyzed, and the recovery of the potentials and the Jost solutions from the solution to the Marchenko system is described. When the reflection coefficients are zero, some explicit solution formulas are provided for the potentials and the Jost solutions in terms of a pair of constant matrix triplets representing the bound-state information for any number of bound states and any multiplicities. In the reduced case, when the two potentials in the linear system are related to each other through complex conjugation, the corresponding reduced Marchenko integral equation is obtained. The solution to the derivative NLS equation is obtained from the solution to the reduced Marchenko integral equation. The theory presented is illustrated with some explicit examples.
