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Semirational solutions and baseband modulational instability of the AB system in fluid mechanics

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Abstract.

Under investigation in this paper is the AB system describing marginally unstable baroclinic wave packets in geophysical fluids. By means of the n -fold modified Darboux transformation, the semirational solutions in terms of the determinants of the AB system are derived. These solutions, which are a combination of rational and exponential functions, can be used to model the nonlinear superposition of the Akhmediev breathers (or the Kuznetsov-Ma breathers) and the rogue waves. The k -order rogue wave of the AB system is produced by the interaction between the l-order rogue wave with \(\frac{1}{2}(k-l)(k+l+1)\) neighboring elements in the \((k-l)\)-order breathers \((0<l<k)\). The proper values of eigenvalue \( \lambda\) and shift \( S_{0}\) are also the requirement for generating the higher-order rogue waves. The link between the baseband modulational instability and the existence condition of these rogue waves is revealed.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, 102206, Beijing, China

    Lei Wang

  2. School of Electrical and Electronic Engineering, North China Electric Power University, 102206, Beijing, China

    Zi-Zhe Wang

  3. School of Nuclear Science and Engineering, North China Electric Power University, 102206, Beijing, China

    Dong-Yang Jiang

  4. School of Information, Beijing Wuzi University, 101149, Beijing, China

    Feng-Hua Qi

  5. School of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, China

    Rui Guo

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  1. Lei Wang
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  2. Zi-Zhe Wang
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Correspondence to Lei Wang.

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Wang, L., Wang, ZZ., Jiang, DY. et al. Semirational solutions and baseband modulational instability of the AB system in fluid mechanics. Eur. Phys. J. Plus 130, 199 (2015). https://doi.org/10.1140/epjp/i2015-15199-8

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  • DOI: https://doi.org/10.1140/epjp/i2015-15199-8

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