Title：Rogue periodic waves stand for gigantic waves on a periodic background. |
Abstract：The nonlinearSchrodinger equation in the focusing case admits two families of periodic wave solutionsexpressed by the Jacobian elliptic functions dn and cn. Both periodic waves aremodulationally unstable with respect to long-wave perturbations. Exact solutions for therogue periodic waves are constructed by using the explicit expressionsfor the periodic eigenfunctions of theZakharov–Shabat spectral problem andthe Darboux transformations. These exact solutions generalize the classical rogue wave(the so-called Peregrine’s breather). Computations of rogue periodic waves rely onproperties of the nonlinear Schrodinger equation due to its integrability.
