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

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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 multi-peak structures. We find that the transition occurs at a modulational stability region in a low perturbation frequency region.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, People’s Republic of China

    Lei Wang & Min Li

  2. School of Energy Power and Mechanical Engineering, North China Electric Power University, Beijing, 102206, People’s Republic of China

    Zi-Qi Wang & Jian-Hui Zhang

  3. School of Information, Beijing Wuzi University, Beijing, 101149, People’s Republic of China

    Feng-Hua Qi

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  1. Lei Wang
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Correspondence to Lei Wang.

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Wang, L., Wang, ZQ., Zhang, JH. et al. Stationary nonlinear waves, superposition modes and modulational instability characteristics in the AB system. Nonlinear Dyn 86, 185–196 (2016). https://doi.org/10.1007/s11071-016-2881-3

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