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.
More on the Applied Maths Seminars here .