Higher-order breathers as quasi-rogue waves on a periodic background

We investigate higher-order breathers of the cubic nonlinear Schrodinger equation on a periodic elliptic background. We find that, beyond first order, any arbitrarily constructed breather on a disordered background generates a single-peaked solitary wave. However, on the periodic backgrounds, the so-called quasi-rogue waves are found more common. These are the quasiperiodic breathers that feature distorted side peaks. We construct such higher-order breathers out of constituent first-order breathers with commensurate periods (i.e., as higher-order harmonic waves). In addition to quasiperiodic, we also find fully periodic breathers, when their wavenumbers are harmonic multiples of the background and each other. But they are truly rare, requiring finely tuned parameters. Thus, on a periodic background, we arrive at the paradoxical conclusion that the higher-order quasi-rogue waves are rather common, while the truly periodic breathers are exceedingly rare.

Automated summary

We investigated higher-order breathers of the cubic nonlinear Schrodinger equation on a periodic elliptic background. We found that, beyond first order, any arbitrarily constructed breather on a disordered background generates a single-peaked solitary wave. However, on the periodic backgrounds, the so-called quasi-rogue waves, which are quasiperiodic breathers with distorted side peaks, are more common. We constructed such higher-order breathers using constituent first-order breathers with commensurate periods and also found truly periodic breathers, but they are rare and require finely tuned parameters.