Poster Session

Generation mechanism of rogue waves for the discrete nonlinear Schr\\{o}dinger equation

Min Li
North China Electric Power University
Peoples Rep of China
Co-Author(s):    Tao Xu
In this poster, we study the generation mechanism of rogue waves for the discrete nonlinear Schr\{o}dinger (DNLS) equation from the viewpoint of structural discontinuities. By the Darboux transformation (DT), we derive the analytical breather solutions of the DNLS equation on a plane-wave background. Then, based on the explicit expressions of group and phase velocities, we give the parameteric conditions for the occurence of velocity jumps, which are exactly the conditions for deriving the rogue-wave solution via the generalized DT. Furthermore, we verify that the first-order rogue wave can be obtained from the breather solutions at the velocity-jumping point. This work might be helpful for understanding the generation of rogue waves in the DNLS model.