Higher-order breathers as quasi-rogue waves on a periodic background Academic Article uri icon


  • AbstractWe investigate higher-order breathers of the cubic nonlinear Schrdinger 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.

published proceedings


author list (cited authors)

  • Ashour, O. A., Chin, S. A., Nikolic, S. N., & Belic, M. R.

citation count

  • 3

complete list of authors

  • Ashour, Omar A||Chin, Siu A||Nikolic, Stanko N||Belic, Milivoj R

publication date

  • March 2022