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

TL;DR

This paper explores stationary nonlinear waves and their interactions in the AB system, revealing novel wave patterns and stability characteristics relevant to geophysical and optical contexts.

Contribution

It introduces new stationary wave solutions and analyzes their interactions and modulational stability within the AB system, expanding understanding of nonlinear wave dynamics.

Findings

Multiple stationary wave types including multi-peak, M-shaped, and W-shaped solitons.

Novel interaction patterns such as antidark soliton to W-shaped soliton conversion.

Transition to stability occurs at low perturbation frequencies.

Abstract

We study the AB system describing marginally unstable baroclinic wave packets in geophysical fluids and also ultra-short 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 non-propagating 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 solion pair, (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.