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Nonlinear Dynamics

, Volume 88, Issue 3, pp 1883–1889 | Cite as

Recurrence behavior for controllable excitation of rogue waves in a two-dimensional \(\varvec{\mathcal {PT}}\)-symmetric coupler

  • Yu Zhu
  • Wei Qin
  • Ji-tao Li
  • Jin-zhong Han
  • Chao-qing Dai
  • Yue-yue Wang
Original Paper

Abstract

A (2 + 1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation with different diffractions in parity-time symmetric coupler is studied, and exact solutions in the form of two-component Peregrine solution and rogue wave triplet are derived. Based on these solutions, by adjusting the relation between the maximal value \(Z_\mathrm{m}\) and the exciting location values \(Z_0\) for Peregrine solution and \(Z_1,Z_2\) for rogue wave triplet, recurrence behaviors for controllable excitation of Peregrine solution and rogue wave triplet including complete excitation, peak excitation, rear excitation and initial excitation are discussed in the exponential diffraction decreasing system. This phenomenon of recurrence for controllable excitation is owing to different values of diffractions in two transverse directions.

Keywords

\(\mathcal {PT}\)-symmetric coupler Recurrence behavior Peregrine solution Rogue wave triplet Exponential diffraction decreasing system 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (11604395 and 11404289), the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China (2016GGJS-135), the High-level Talents Research and Startup Foundation Projects for Doctors of Zhoukou Normal University (zknu2014120), and the School-based Program of Zhoukou Normal University (zknuB1201605).

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.School of Physics and Telecommunications EngineeringZhoukou Normal UniversityZhoukouPeople’s Republic of China
  2. 2.School of SciencesZhejiang A&F UniversityLin’anPeople’s Republic of China

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