Prof. Dmitry Pelinovsky (McMaster University, Canada)
Title: Rogue periodic waves in the focusing MKDV and NLS equations
Abstract: Rogue periodic waves stand for gigantic waves on a periodic background. The nonlinear Schrodinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov–Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine’s breather). Computations of rogue periodic waves rely on properties of the nonlinear Schrodinger equation due to its integrability.
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