Abstract:
We investigate an AB system, which can be used to describe marginally unstable baroclinic wave packets in a geophysical fluid. Using the generalized Darboux transformation, we obtain higher-order rogue wave solutions and analyze rogue wave propagation and interaction. We obtain bright rogue waves with one and two peaks. For the wave packet amplitude and the mean-flow correction resulting from the self-rectification of the nonlinear wave, the positions and values of the wave crests and troughs are expressed in terms of a parameter describing the state of the basic flow, in terms of a parameter responsible for the interaction of the wave packet and the mean flow, and in terms of the group velocity. We show that the interaction of the wave packet and mean flow and also the group velocity affect the propagation and interaction of the amplitude of the wave packet and the self-rectification of the nonlinear wave.
This research was supported by the National Natural
Science Foundation of China (Grant No. 11272023), the Open Fund of State Key
Laboratory of Information Photonics and Optical Communications, Beijing
University of Posts and Telecommunications (Grant No. IPOC2013B008), and the Foundation of Hebei Education Department of China (Grant No. QN2015051).