Extraction of Solitary Wave Features to the Heisenberg Ferromagnetic Spin Chain and the Complex Klein–Gordon Equations

  • K. M. Abdul Al WoadudEmail author
  • Dipankar Kumar
  • Md. Jahirul Islam
  • Md. Imrul Kayes
  • Amit Kumar Kundu
Original Paper


In this paper, the modified Kudryashov method is applied for obtaining the exact travelling wave solutions for the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation and the complex Klein–Gordon equation. The extracted solutions show distinct physical configurations. More precisely, the modified Kudryashov method is utilized for constructing the exact periodic and soliton solutions of these equations. As an outcome, in a broader sense, dark, bright, dark-bright, singular or combined singular and optical soliton solutions or wave features are derived from the equations. All solitons are verified through the corresponding equations with the help of Maple package program. The three-dimensional and two-dimensional waves are generated with the help of MATLAB for investigating the real significance of the proposed scheme to draw all solutions.


Heisenberg ferromagnetic spin chain equation Complex Klein–Gordon equation Modified Kudryashov method New exact traveling wave solutions Symbolic computation 



The authors would like to thank Mohammed Khurshed Alam of department of Electrical and Electronic Engineering, Uttara University for his valuable suggestions in preparing the manuscript.


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Copyright information

© Springer Nature India Private Limited 2019

Authors and Affiliations

  • K. M. Abdul Al Woadud
    • 1
    Email author
  • Dipankar Kumar
    • 2
  • Md. Jahirul Islam
    • 1
  • Md. Imrul Kayes
    • 3
  • Amit Kumar Kundu
    • 1
  1. 1.Department of Electrical and Electronic EngineeringUttara UniversityDhakaBangladesh
  2. 2.Department of MathematicsBangabandhu Sheikh Mujibur Rahman Science and Technology UniversityGopalganjBangladesh
  3. 3.Department of Civil EngineeringUttara UniversityDhakaBangladesh

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