J. Chen, D.E. Pelinovsky, and R.E. White
Rogue waves on the periodic wave background in the focusing nonlinear Schrodinger equation
We present exact solutions for rogue waves arising on the background of periodic waves
in the focusing nonlinear Schrodinger equation. The exact solutions are obtained by characterizing
the Lax spectrum related to the periodic waves and by using the one-fold Darboux transformation.
The magnication factor of the rogue waves is computed in the closed analytical form. We relate
explicitly the rogue wave solutions to the modulation instability of the periodic wave background.
nonlinear Schrodinger equation, periodic travelling waves, rogue waves, Lax spectrum, modulation instability.