Modulational instability of periodic standing waves in the derivative NLS equation

Abstract

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.

arXiv comment30 pages; 6 figures

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• The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation
• On the stability of periodic waves for the cubic derivative NLS and the quintic NLS
• Periodic traveling waves in the ϕ^4 model: Instability, stability and localized structures