J. Chen and D.E. Pelinovsky
Rogue waves on the background of periodic standing waves in the derivative
nonlinear Schrodinger equation
Physical Review E 103 (2021), 062206 (25 pages)
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.
Keywords:
derivative nonlinear Schrodinger equation, periodic standing waves,
modulational instability, algebraic solitons, rogue waves.