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We consider the periodic standing waves in the derivative nonlinearSchrodinger (DNLS) equation arising in plasma physics. By using a newlydeveloped algebraic method with two eigenvalues, we classify all periodicstanding waves in terms of eight eigenvalues of the Kaup-Newell spectralproblem located at the end points of the spectral bands outside the real line.The analytical work is complemented with the numerical approximation of thespectral bands, this enables us to fully characterize the modulationalinstability of the periodic standing waves in the DNLS equation.

Modulational instability of periodic standing waves in the derivative NLS equation