Effect of a small loss or gain in the periodic nonlinear Schrodinger anomalous wave dynamics

The focusing nonlinear Schrodinger (NLS) equation is one of the mathematical models describing the generation of anomalous (rogue) waves (AWs) in nature due to modulation instability. In real physical application it is important to take into account the effect of non-integrable corrections to the model. In the simplest case of a single unstable mode we provide simple analytic formulas describing the effect of small loss or gain on dynamics of the spectral curves and the corresponding near-degenerate tori. We show that very small loss or gain may seriously affect the recurrence of anomalous waves. As a corollary, we theoretically explain some effects observed in water tank experiments.

^* Zoom Meeting ID: 979 5396 3790