Nonlinear Dynamics

, Volume 86, Issue 1, pp 185–196 | Cite as

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

  • Lei Wang
  • Zi-Qi Wang
  • Jian-Hui Zhang
  • Feng-Hua Qi
  • Min Li
Original Paper


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.


AB system Stationary nonlinear waves Breather–soliton dynamics Nonlinear wave interactions Modulational instability 



We express our sincere thanks to all the members of our discussion group for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant (Nos. 11305060 and 61505054), by the Fundamental Research Funds of the Central Universities (Project No. 2015ZD16), by the Innovative Talents Scheme of North China Electric Power University and by the Higher-Level Item Cultivation Project of Beijing Wuzi University (No. GJB20141001).


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Lei Wang
    • 1
  • Zi-Qi Wang
    • 2
  • Jian-Hui Zhang
    • 2
  • Feng-Hua Qi
    • 3
  • Min Li
    • 1
  1. 1.Department of Mathematics and PhysicsNorth China Electric Power UniversityBeijingPeople’s Republic of China
  2. 2.School of Energy Power and Mechanical EngineeringNorth China Electric Power UniversityBeijingPeople’s Republic of China
  3. 3.School of InformationBeijing Wuzi UniversityBeijingPeople’s Republic of China

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