We extend the global existence result for the derivative NLS equation to the case when the initial datum includes a finite number of solitons. This is achieved by an application of the B\"{a}cklund transformation that removes a finite number of zeros of the scattering coefficient. By means of this transformation, the Riemann--Hilbert problem for meromorphic functions can be formulated as the one for analytic functions, the solvability of which was obtained recently.

中文翻译：

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导数 NLS 方程：孤子全局存在

我们将导数 NLS 方程的全局存在结果扩展到初始数据包含有限数量孤子的情况。这是通过应用 B\"{a}cklund 变换来实现的，该变换去除了散射系数的有限数量的零。通过这种变换，亚纯函数的黎曼-希尔伯特问题可以表述为解析函数，其可解性是最近获得的。