Construction of solitary wave solutions of some nonlinear dynamical system arising in nonlinear water wave models

  • Aly R. SeadawyEmail author
  • Dianchen Lu
  • Naila Nasreen
Original Paper


The higher order of nonlinear partial differential equations in mathematical physics is studied. We used the analytical mathematical methods of the nonlinear (3+1)-dimensional extended Zakharov–Kuznetsov dynamical, modified KdV–Zakharov–Kuznetsov and generalized shallow water wave equations to demonstrate the efficiency and validity of the proposed powerful technique. The shallow water wave models have been applied in tidal waves and weather simulation. Exact wave solutions of these models in various forms such as Kink and anti-Kink solitons, bright–dark soliton, solitary wave and periodic solutions are constructed that have plenty of applications in diverse areas of physics. Graphically, we presented the movement of some obtained solitary wave solutions that aids in understanding the physical phenomena of these models.


Extended Zakharov–Kuznetsov dynamical model Modified KdV–Zakharov–Kuznetsov model Generalized (3+1) shallow water Solitons Solitary wave solutions 


02.30.Jr 05.45.Yv 47.10.A 47.35.+i 47.35.Fg 


Compliance with ethical standards

Competing interests

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors. The authors did not have any competing interests in this research.


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Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceTaibah UniversityMedinaSaudi Arabia
  2. 2.Faculty of ScienceJiangsu UniversityZhenjiangPeople’s Republic of China

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