Nonlinear Dynamics

, Volume 95, Issue 1, pp 669–684 | Cite as

Application of the ITEM for solving three nonlinear evolution equations arising in fluid mechanics

  • Cevat Teymuri Sendi
  • Jalil ManafianEmail author
  • Hasan Mobasseri
  • Mohammad Mirzazadeh
  • Qin Zhou
  • Ahmet Bekir
Original Paper


In this paper, by introducing new approach, the improved \(\tan \left( \phi (\xi )/2\right) \)-expansion method (ITEM) is further extended into the Vakhnenko–Parkes (VP) equation, the generalized regularized-long-wave (GRLW) equation and the symmetric regularized-long-wave (SRLW) equation in fluid mechanic. We extended the ITEM proposed by Manafian et al. (Int J Appl Comput Math 2:243–268, 2016) to construct new types of soliton wave solutions of nonlinear partial differential equations (NPDEs). The merit of the presented method is finding the further solutions of the considering problems including soliton, periodic, kink and kink-singular wave solutions. Comparing our new results with other results shows that our results give the further solutions. The results of applying this procedure (Figs. 1, 2, 3, 4, 5, 6) to the studied cases show the high efficiency of the new technique. Finally, these solutions might play an important role in engineering, physics and applied mathematics fields.


Improved \(\tan (\phi (\xi )/2)\)-expansion method Vakhnenko–Parkes equation Generalized regularized-long-wave equation Symmetric regularized-long-wave equation 

Mathematics Subject Classification

35Q79 35Q51 35Q35 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Tabriz BranchIslamic Azad UniversityTabrizIran
  2. 2.Young Researchers and Elite Club, Ilkhchi BranchIslamic Azad UniversityIlkhchiIran
  3. 3.Department of Management, Science and Research BranchIslamic Azad UniversityTehranIran
  4. 4.Department of Engineering Sciences, Faculty of Technology and Engineering, East of GuilanUniversity of GuilanRudsar-VajargahIran
  5. 5.School of Electronics and Information EngineeringWuhan Donghu UniversityWuhanPeople’s Republic of China
  6. 6.Neighbourhood of AkcaglanEskisehirTurkey

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