Rogue waves on the background of periodic standing waves in the derivative NLS equation

Abstract

The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the DNLS equation. We show that the space-time localization of a rogue wave is only possible if the periodic standing wave is modulationally unstable. If the periodic standing wave is modulationally stable, the rogue wave solutions degenerate into algebraic solitons propagating along the background and interacting with the periodic standing waves. Maximal amplitudes of rogue waves are found analytically and confirmed numerically.

arXiv comment33 pages; 10 figures; 9 appendices

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• The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation
• Broader Universality of Rogue Waves of Infinite Order
• Nonlinear bandgap transmission by discrete rogue waves induced in a pendulum chain
• Numerical inverse scattering transform for the derivative nonlinear Schrodinger equation
• The data-driven localized wave solutions of the derivative nonlinear Schrodinger equation by using improved PINN approach