论文标题
非线性schrödinger方程，强迫涉及本征functions的产品
The nonlinear Schrödinger equation with forcing involving products of eigenfunctions
论文作者
论文摘要
我们详细介绍了一种新方法，该方法从一个空间维度的可集成演化方程开始，它构建了该方程式的可集成强制版本。强迫包括涉及相关兰克斯对某些征征的二次产物的术语。值得注意的是，其中一些强制方程在重要的物理现象的建模中出现。这些方程的初始值问题可以作为Riemann-Hilbert问题进行表述，其中“跳跃矩阵”具有显式X和T依赖性，并且可以根据初始数据进行计算。因此，这些方程式可以像从中生成的非线性集成方程一样有效地求解。给出了非线性Schrodinger强制版本的详细信息。
We elaborate on a new methodology, which starting with an integrable evolution equation in one spatial dimension, constructs an integrable forced version of this equation. The forcing consists of terms involving quadratic products of certain eigenfunctions of the associated Lax pair. Remarkably, some of these forced equations arise in the modelling of important physical phenomena. The initial value problem of these equations can be formulated as a Riemann-Hilbert problem, where the "jump matrix" has explicit x and t dependence and can be computed in terms of the initial data. Thus, these equations can be solved as efficiently as the nonlinear integrable equations from which they are generated. Details are given for the forced versions of the nonlinear Schrodinger.
