论文标题
Korteweg-de Vries方程的二进制Darboux转换的连续类似物
A continuous analog of the binary Darboux transformation for the Korteweg-de Vries equation
论文作者
论文摘要
在KDV上下文中，我们提出了二进制Darboux转换的连续版本（又称双换向方法）。我们的方法基于Riemann-Hilbert问题，并产生了一种新的明确公式，以扰动宽类级型电势的负频谱，而无需更改其余的散射数据。这扩展了先前已知的公式，用于将有限的许多状态插入/删除任意性质的负频谱集。在KDV上下文中，我们的方法提供了与古典二进制Darboux转换相同的好处。
In the KdV context we put forward a continuous version of the binary Darboux transformation (aka the double commutation method). Our approach is based on the Riemann-Hilbert problem and yields a new explicit formula for perturbation of the negative spectrum of a wide class of step-type potentials without changing the rest of the scattering data. This extends the previously known formulas for inserting/removing finitely many bound states to arbitrary sets of negative spectrum of arbitrary nature. In the KdV context our method offers same benefits as the classical binary Darboux transformation does.
