J. Chen, D.E. Pelinovsky, and R.E. White
Periodic standing waves in the focusing nonlinear Schrodinger
equation: Rogue waves and modulation instability
Physica D 405 (2020) 132378 (13 pages)
Abstract:
We present exact solutions for rogue waves arising on the background of periodic standing waves in
the focusing nonlinear Schrodinger equation. The exact solutions are obtained by characterizing the Lax
spectrum related to the periodic standing waves and by using the one-fold Darboux transformation.
The magnification factor of the rogue waves is computed in the closed analytical form. We relate the
rogue wave solutions to the modulation instability of the background of the periodic standing waves.
Keywords:
nonlinear Schrodinger equation, periodic travelling waves, rogue waves, Lax spectrum, modulation instability.