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

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,...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2016-10, Vol.86 (1), p.185-196
Main Authors: Wang, Lei, Wang, Zi-Qi, Zhang, Jian-Hui, Qi, Feng-Hua, Li, Min
Format: Article
Language:English
Subjects:
Automotive Engineering
Baroclinic waves
Classical Mechanics
Control
Dynamical Systems
Engineering
Frequency stability
Geophysical fluids
Geophysics
Instability
Mechanical Engineering
Nonlinear dynamics
Nonlinear optics
Nonlinearity
Original Paper
Perturbation
Solitary waves
Solitons
Stability
Structural stability
Superposition (mathematics)
Vibration
Wave packets
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 multi-peak structures. We find that the transition occurs at a modulational stability region in a low perturbation frequency region.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-016-2881-3