In this paper, we derive solutions to the derivative nonlinear Schrödinger equation, which are associated to real and complex discrete eigenvalues of the Kaup–Newell spectral problem. These solutions are obtained by investigating double Wronskian solutions of the coupled Kaup–Newell equations and their reductions by means of bilinear method and a reduction technique. The reduced equations include the derivative nonlinear Schrödinger equation and its nonlocal version. Some obtained solutions allow not only periodic behavior, but also solitons on periodic background. Dynamics are illustrated.

中文翻译：

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孤子到微分非线性薛定谔方程：双 Wronskians 和归约

在本文中，我们推导了导数非线性薛定谔方程的解，该方程与 Kaup-Newell 谱问题的实数和复数离散特征值相关联。这些解是通过研究耦合 Kaup-Newell 方程的双 Wronskian 解及其通过双线性方法和归约技术的归约获得的。简化方程包括导数非线性薛定谔方程及其非局部版本。一些获得的解决方案不仅允许周期性行为，还允许周期性背景上的孤子。说明了动力学。