Phase shift, oscillation and collision of the anti-dark solitons for the (3+1)-dimensional coupled nonlinear Schrödinger equation in an optical fiber communication system

  • Weitian Yu
  • Wenjun LiuEmail author
  • Houria Triki
  • Qin Zhou
  • Anjan Biswas
Original Paper


In the long-distance optical fiber communication system, we consider the (3+1)-dimensional coupled nonlinear Schrödinger equation with perturbation functions, which controls the transverse effects, because of the complexity of nonlinear phenomena. Anti-dark two-soliton solutions are derived by the Hirota method. The perturbation function representing the dissipation rate is discussed. Five different transmission structures of solitons are presented. Besides, their propagation and collision dynamics are analyzed. Control methods for phase shift and oscillation are also suggested. We hope results in this paper are of guiding significance to the research of phase shifters, optical logic devices and ultrashort pulse lasers.


Anti-dark solitons Soliton collision Analytic solution Hirota method Nonlinear Schrödinger equation 



We acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 11674036 and 11875008), by the Beijing Youth Top-notch Talent Support Program (Grant No. 2017000026833ZK08), and by the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Grant No. IPOC2017ZZ05).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.State Key Laboratory of Information Photonics and Optical Communications, and School of ScienceBeijing University of Posts and TelecommunicationsBeijingPeople’s Republic of China
  2. 2.Radiation Physics Laboratory, Department of Physics, Faculty of SciencesBadji Mokhtar UniversityAnnabaAlgeria
  3. 3.School of Electronics and Information EngineeringWuhan Donghu UniversityWuhanPeople’s Republic of China
  4. 4.Department of Physics, Chemistry and MathematicsAlabama A & M UniversityNormalUSA
  5. 5.Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  6. 6.Department of Mathematics and StatisticsTshwane University of TechnologyPretoriaSouth Africa

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