Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system

Abstract

We study the AB system describing marginally unstable baroclinic wave packets in geophysical fluids and also ultrashort pulses in nonlinear optics. We show that the breather can be converted into different types of stationary nonlinear waves on constant backgrounds, including the multi-peak soliton, M-shaped soliton, W-shaped soliton and periodic wave. We also investigate the nonlinear interactions between these waves, which display some novel patterns due to the nonpropagating characteristics of the solitons: (1) Two antidark solitons can produce a W-shaped soliton instead of a higher-order antidark one; (2) the interaction between an antidark soliton and a W-shaped soliton can not only generate a higher-order antidark soliton, but also form a W-shaped soliton pair; and (3) the interactions between an oscillation W-shaped soliton and an oscillation M-shaped soliton show the multipeak structures. We find that the transition occurs at a modulational stability region in a low perturbation frequency region.

W-shaped soliton complexes and rogue-wave pattern transitions for the AB system

“…Wang et al discussed the breather/rogue-to-soliton properties and nonlinear wave interactional solutions of Eq. (1) [34]. In addition, Chow et al generalized Eq.…”

“…Here we note that, dynamics of the Peregrine rogue waves and the first-order W-shaped soliton in the component A have been studied in Refs. [31][32][33][34], so here we omit presenting them and just concentrate on the higher-order W-shaped solitons in the rest of this paper.…”