**SMS scnews item created by Eduardo Altmann at Tue 27 Feb 2018 0813**

Type: Seminar

Distribution: World

Expiry: 14 Mar 2018

**Calendar1: 14 Mar 2018 1400-1500**

**CalLoc1: AGR Carslaw 829**

CalTitle1: Rogue periodic waves in the focusing MKDV and NLS equations

Auth: ega@dora.maths.usyd.edu.au

### Applied Maths Seminar

# ogue periodic waves in the focusing MKDV and NLS equations

### Pelinovsky

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 Zakharovâ€“Shabat spectral problem and
the Darboux transformations. These exact solutions generalize the classical rogue wave
(the so-called Peregrineâ€™s breather). Computations of rogue periodic waves rely on
properties of the nonlinear Schrodinger equation due to its integrability.

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