Nonlinear Dynamics

, Volume 95, Issue 1, pp 369–380 | Cite as

One-soliton shaping and two-soliton interaction in the fifth-order variable-coefficient nonlinear Schrödinger equation

  • Chunyu Yang
  • Wenjun LiuEmail author
  • Qin ZhouEmail author
  • Dumitru Mihalache
  • Boris A. Malomed
Original Paper


One- and two-soliton analytical solutions of a fifth-order nonlinear Schrödinger equation with variable coefficients are derived by means of the Hirota bilinear method in this paper. Various scenarios of one-soliton shaping and two-soliton interaction and reshaping are investigated, using the obtained exact solutions and adjusting parameters of the underlying model. We find that widths of two colliding solitons can change without changing their amplitudes. Furthermore, we produce a solution in which two originally bound solitons are separated and are then moving in opposite directions. We also show that two colliding solitons can fuse to form a spatiotemporal train, composed of equally separated identical pulses. Moreover, we display that the width and propagation direction of the spatiotemporal train can change simultaneously. Effects of corresponding parameters on the one-soliton shaping and two-soliton interaction are discussed. Results of this paper may be beneficial to the application of optical self-routing, switching and path control.


Soliton shaping Soliton interaction Soliton manipulation Fifth-order variable-coefficient nonlinear Schrödinger equation 



This work was supported by the National Natural Science Foundation of China (Grant Nos. 11875008 and 11674036), 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 Nos. IPOC2016ZT04 and IPOC2017ZZ05). The work of Qin Zhou was supported by the National Natural Science Foundation of China (Grant Nos. 11705130 and 1157149), and this author was also sponsored by the Chutian Scholar Program of Hubei Government in China.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Information Photonics and Optical Communications, and School of ScienceBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.School of Electronics and Information EngineeringWuhan Donghu UniversityWuhanPeople’s Republic of China
  3. 3.Horia Hulubei National Institute for Physics and Nuclear EngineeringMagureleRomania
  4. 4.Department of Physical Electronics, School of Electrical Engineering, Faculty of EngineeringTel Aviv UniversityTel AvivIsrael

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