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

  • Lei WangEmail author
  • Zi-Zhe Wang
  • Dong-Yang Jiang
  • Feng-Hua Qi
  • Rui Guo
Regular Article

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.

Keywords

Soliton Modulational Instability Rogue Wave Neighboring Element Conforti 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Lei Wang
    • 1
    Email author
  • Zi-Zhe Wang
    • 2
  • Dong-Yang Jiang
    • 3
  • Feng-Hua Qi
    • 4
  • Rui Guo
    • 5
  1. 1.Department of Mathematics and PhysicsNorth China Electric Power UniversityBeijingChina
  2. 2.School of Electrical and Electronic EngineeringNorth China Electric Power UniversityBeijingChina
  3. 3.School of Nuclear Science and EngineeringNorth China Electric Power UniversityBeijingChina
  4. 4.School of InformationBeijing Wuzi UniversityBeijingChina
  5. 5.School of MathematicsTaiyuan University of TechnologyTaiyuanChina

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