Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation

We consider the periodic standing waves in the derivative nonlinear Schrodinger (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.

Automated summary

In this study, periodic standing waves in the derivative nonlinear Schrodinger equation in plasma physics are classified using an algebraic method with two eigenvalues. The eight eigenvalues of the Kaup-Newell spectral problem at the end points of the spectral bands outside the real line are used for classification. Analytical work is complemented with numerical approximation to fully characterize the modulational instability of the periodic standing waves in the DNLS equation.