Published: Sept. 14, 2021
Justin Cole, Department of Mathematics, University of Colorado Colorado Springs

Transverse Instability of Rogue Waves

Rogue waves, or “freak waves”, are large amplitude waves that suddenly appear and then disappear. Originally the subject of folklore, these waves have now been successfully observed in numerous physical systems such as deep water waves and fiber optics. A typical rogue wave model is the one space, one time (1+1) nonlinear Schrodinger (NLS) equation and the Peregrine soliton solution which has a peak height three times that of the background. However, in deep water a more complete description is that of the 2+1 hyperbolic NLS equation with two significant transverse dimensions. It is shown that the Peregrine soliton is transversely unstable to both long and short wavelength perturbations of finite size. Moreover, the instability spectrum is found to coincide with that of the background plane wave.

Recorded video of this seminar is available (click this link).