Resonant multi-soliton solutions to new (3+1)-dimensional Jimbo–Miwa equations by applying the linear superposition principle

  • Chun-Ku KuoEmail author
  • Behzad Ghanbari
Original Paper


In this paper, the linear superposition principle and Hirota bilinear equations are simultaneously employed to handle two new (3+1)-dimensional Jimbo–Miwa equations. The corresponding resonant multi-soliton solutions and the related wave numbers are formally established, which are totally different from the previously reported ones. Moreover, the extracted N-soliton waves and dispersion relations have distinct physical structures compared to solutions obtained by Wazwaz. Finally, five graphical representations are portrayed by taking definite values to free parameters which demonstrates various versions of traveling solitary waves. The results show the proposed approach provides enough freedom to construct multi-soliton waves that may be related to a large variety of real physical phenomena and, moreover, enriches the solution structure.


Linear superposition principle Hirota bilinear equation New (3+1)-dimensional Jimbo–Miwa equation Multi-soliton Dispersion relations 



We are most grateful to the anonymous referees for the help in improving the original manuscript. And it is gratefully acknowledged that this work was supported by the Ministry of National Defense, R.O.C.

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. 2019

Authors and Affiliations

  1. 1.Department of Aeronautics and AstronauticsAir Force AcademyKaohsiungTaiwan, ROC
  2. 2.Department of Engineering ScienceKermanshah University of TechnologyKermanshahIran

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