Nonlinear Dynamics

, Volume 80, Issue 1–2, pp 715–721 | Cite as

Controllable combined Peregrine soliton and Kuznetsov–Ma soliton in \({\varvec{\mathcal {PT}}}\)-symmetric nonlinear couplers with gain and loss

  • Chao-Qing Dai
  • Yue-Yue Wang
Original Paper


We investigate a (2+1)-dimensional-coupled variable coefficient nonlinear Schrödinger equation in parity time symmetric nonlinear couplers with gain and loss and analytically obtain a combined structure solution via the Darboux transformation method. When the imaginary part of the eigenvalue \(n\) is smaller or bigger than 1, we can obtain the combined Peregrine soliton and Akhmediev breather, or Kuznetsov–Ma soliton, respectively. Moreover, we study the controllable behaviors of this combined Peregrine soliton and Kuznetsov–Ma soliton structure in a diffraction decreasing system with exponential profile. In this system, the effective propagation distance \(Z\) exists a maximal value \(Z_m\) and the maximum amplitude of the KM soliton appears in the periodic locations \(Z_{i}\). By modulating the relation between values of \(Z_m\) and \(Z_i\), we realize the control for the excitation of the combined Peregrine soliton and Kuznetsov–Ma soliton, such as the restraint, maintenance, and postpone.


\({\mathcal {PT}}\)-symmetric nonlinear couplers (2+1)-dimensional-coupled nonlinear Schrödinger equation Combined Peregrine soliton and Kuznetsov–Ma soliton Controllable behavior 



This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY13F050006), the National Natural Science Foundation of China (Grant Nos. 11375007 and 11404289), and the Scientific Research and Developed Fund of Zhejiang A & F University (Grant No. 2014FR020). Dr. Chao-Qing Dai is also sponsored by the Foundation of New Century “151 Talent Engineering” of Zhejiang Province of China and Youth Top-notch Talent Development and Training Program of Zhejiang A & F University.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of SciencesZhejiang A & F UniversityLin’anPeople’s Republic of China
  2. 2.Key Laboratory of Chemical Utilization of Forestry Biomass of Zhejiang ProvinceZhejiang A & F UniversityLin’anPeople’s Republic of China

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