We consider the periodic standing waves in the derivative nonlinear Schrödinger (DNLS) equation arising in plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all periodic standing waves in terms of eight eigenvalues of the Kaup–Newell spectral problem located at the end points of the spectral bands outside the real line. The analytical work is complemented with the numerical approximation of the spectral bands, this enables us to fully characterize the modulational instability of the periodic standing waves in the DNLS equation.

中文翻译：

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NLS导数方程中周期驻波的调制不稳定性

我们考虑等离子体物理中产生的导数非线性Schrödinger（DNLS）方程中的周期性驻波。通过使用具有两个特征值的新开发的代数方法，我们根据位于实线之外的光谱带端点的Kaup–Newell光谱问题的八个特征值对所有周期性驻波进行分类。分析工作与光谱带的数值近似相辅相成，这使我们能够充分表征DNLS方程中周期性驻波的调制不稳定性。