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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
  • 31 Downloads

Abstract

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.

Keywords

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

PACS Nos.

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

Notes

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.

References

  1. [1]
    M J Ablowitz and P A Clarkson Solitons, Nonlinear Evolution Equations and Inverse Scattering (New York: Cambridge University Press) (1991)zbMATHCrossRefGoogle Scholar
  2. [2]
    P K Shukla and A A Mamun Introduction to Dusty Plasma Physics (Bristol, UK: Institute of Physics Publishing) (2002)CrossRefGoogle Scholar
  3. [3]
    S A El-Tantawy and W M Moslem Phys Plasmas 21 052112 (2014)ADSCrossRefGoogle Scholar
  4. [4]
    M B Kochanov, N A Kudryashov and D I Sinel’shchikov J Appl Math Mech 77 25 (2013)MathSciNetCrossRefGoogle Scholar
  5. [5]
    N Nasreen, D Lu and M Arshad Optik 161 221 (2018)ADSCrossRefGoogle Scholar
  6. [6]
    D Lu, A R Seadawy, M Arshad and J Wang Results in Physics 7 899 (2017)ADSCrossRefGoogle Scholar
  7. [7]
    A R Seadawy, M Arshad and D Lu Eur. Phys. J. Plus 132 162 (2017)CrossRefGoogle Scholar
  8. [8]
    Z M Liu, W S Duan and G J He Phys Plasmas 15 083702 (2008)ADSCrossRefGoogle Scholar
  9. [9]
    A R Seadawy Phys Plasmas 21 052107 (2014)ADSCrossRefGoogle Scholar
  10. [10]
    H Sarfraz and U Saleem Modern Physics Letters A 32 1750196 (2017)ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    A R Seadawy and D Lu Result Phys 6 560 (2016)ADSCrossRefGoogle Scholar
  12. [12]
    F Demontis Theoret Math Phys 168 886 (2011)MathSciNetCrossRefGoogle Scholar
  13. [13]
    M Eslami Nonlinear Dynamics 85 813 (2016)MathSciNetCrossRefGoogle Scholar
  14. [14]
    M Eslami and M Mirzazadeh Ocean Engineering 83 133 (2014)CrossRefGoogle Scholar
  15. [15]
    M Eslami, A Neyrame and M Ebrahimi Journal of King Saud University - Science 24 69 (2012)CrossRefGoogle Scholar
  16. [16]
    M Mirzazadeh, M Eslami and A H Arnous European Physical Journal Plus 130 4 (2015)ADSCrossRefGoogle Scholar
  17. [17]
    F S Khodadad, F Nazari, M Eslami and H Rezazadeh Optical and Quantum Electronics 49 384 (2017)CrossRefGoogle Scholar
  18. [18]
    M Mirzazadeh, M Eslami and A Biswas Computational and Applied Mathematics 33 831 (2014)MathSciNetCrossRefGoogle Scholar
  19. [19]
    J G Liu, M Eslami, H Rezazadeh and M Mirzazadeh Nonlinear Dynamics 95 1027 (2019)CrossRefGoogle Scholar
  20. [20]
    Aly seadawy and Nadia Cheemaa Indian Journal of Physics (2019) https://doi.org/10.1007/s12648-019-01442-6
  21. [21]
    Rabab Shahein and Aly seadawy Indian Journal of Physics 93 (2019) 941–949ADSCrossRefGoogle Scholar
  22. [22]
    Aly seadawy, Dianchen Lu and Muhammad Arshad Indian Journal of Physics 93 (2019) 1041–1049ADSCrossRefGoogle Scholar
  23. [23]
    Aly R. Seadawy, Mujahid Iqbal and Dianchen Lu Indian Journal of Physics (2019). https://doi.org/10.1007/s12648-019-01500-z CrossRefGoogle Scholar
  24. [24]
    Aly R. Seadawy, Mujahid Iqbal and Dianchen Lu Indian Journal of Physics (2019). https://doi.org/10.1007/s12648-019-01532-5 CrossRefGoogle Scholar
  25. [25]
    M N Ali, A R Seadawy and S M Husnine Modern Physics Letters A 34 1950027 (2019) ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    M A Helal and A R Seadawy Computers and Mathematics with Applications 64 3557 (2012)MathSciNetCrossRefGoogle Scholar
  27. [27]
    M H Islam, K Khan, M A Akbar and M A Salam SpringerPlus 3 105 (2014)CrossRefGoogle Scholar
  28. [28]
    F Mahmud, M Samsuzzoha and M A Akbar Results in Physics 7 4296 (2017)ADSCrossRefGoogle Scholar
  29. [29]
    K Khan and M A Akbar Mathematical Methods in Applied Sciences 39 2752 (2016)ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    M G Hafez, M N Alam and M A Akbar Results Phys 4 177 (2014)ADSCrossRefGoogle Scholar
  31. [31]
    M M Miah, H M S Ali, M A Akbar and A M Wazwaz The European Physical Journal Plus 132 252 (2017)ADSCrossRefGoogle Scholar
  32. [32]
    M A Akbar, N H M Ali and R Roy Results in Physics 9 1031 (2018)ADSCrossRefGoogle Scholar
  33. [33]
    M A Huda, M A Akbar and S S Shanta Journal of Ocean engineering and Science 3 1 (2018)CrossRefGoogle Scholar
  34. [34]
    V I Petviashvili and O V Pokhotelov Solitary Waves in Plasmas and in the Atmosphere (Moscow: Energoatomizdat) (1989)zbMATHGoogle Scholar
  35. [35]
    D E Pelinovsky, Y A Stepanyants and Y S Kivshar Phys. Rev. E 51 5016 (1995)ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    E Falcon, C Laroche and S Fauve Phys. Rev. Lett. 89 204501 (2002)ADSCrossRefGoogle Scholar
  37. [37]
    B G Zhang, Z R Liu and Q Xiao Appl Math Comput 217 392 (2010)MathSciNetGoogle Scholar
  38. [38]
    G W Wang, T Z Xu, S Johnson and A Biswas Asterophys Space Sci 349 317 (2014)ADSCrossRefGoogle Scholar
  39. [39]
    M Iqbal, A R Seadawy and D Lu Modern Physics Letters A 33 1850217 (2018)ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    M Arshad, A R Seadawy, D Lu and J Wang Chinese J. phys. 55 780 (2017)ADSCrossRefGoogle Scholar
  41. [41]
    X Y Wen Appl Math Comput 217 1367 (2010)MathSciNetGoogle Scholar
  42. [42]
    G Xu and L Zhibin Chaos Solitons Fractals 24 549 (2005)ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    J G Liu and Y He Nonlinear Dynam. 90 363 (2017)MathSciNetCrossRefGoogle Scholar
  44. [44]
    X Yu, Y T Gao, Y Z Sun and Y Liu Phys Scr 81 045402 (2010)ADSCrossRefGoogle Scholar
  45. [45]
    R Hirota Phys Rev Lett 27 1192 (1971)ADSCrossRefGoogle Scholar
  46. [46]
    M A Abdou Appl Math Comput 190 988 (2007)MathSciNetGoogle Scholar
  47. [47]
    Y Yuqin Chaos Solitons Fractals 24 301 (2005)ADSCrossRefGoogle Scholar
  48. [48]
    Z Xin and W D Shan Appl Math Comput 212 296 (2009)MathSciNetGoogle Scholar
  49. [49]
    B Tian and Y T Gao Comput. Phys. Comm. 95 139 (1996)ADSCrossRefGoogle Scholar
  50. [50]
    D Lu, A R Seadawy, M. Arshad and Jun Wang Results in Physics 7 899 (2017)ADSCrossRefGoogle Scholar
  51. [51]
    K Tariq and A R Seadawy Results in Physics 7 1143 (2017)ADSCrossRefGoogle Scholar
  52. [52]
    U Yavuz, K Dogan and E I Ibrahim Comput Math Appl 61 1278 ( 2011)MathSciNetCrossRefGoogle Scholar
  53. [53]
    S Dinarvand, S Khosravi, A Doosthoseini and M M Rashidi Adv Theor Appl Mech 1 327 (2008)Google Scholar
  54. [54]
    A H Khater, D K Callebaut, M A Helal and A R Seadawy Physica Scripta 74 384 (2006)ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    M Arshad, A R Seadawy and D Lu The European Physical Journal Plus 132 371 (2017)ADSCrossRefGoogle Scholar
  56. [56]
    A R Seadawy European Physical Journal Plus 132 518 (2017)ADSCrossRefGoogle Scholar
  57. [57]
    A R Seadawy International Journal of Computational Methods 15 1850017 (2018)MathSciNetCrossRefGoogle Scholar
  58. [58]
    A R Seadawy and K. El-Rashidy The Pramana - Journal of Physics 87 20 (2016)ADSCrossRefGoogle Scholar
  59. [59]
    A R Seadawy Comput Math Appl 62 (2011)Google Scholar
  60. [60]
    M H Islam, K Khan, M A Akbar and M A Salam Springer Plus 3 105 (2014)CrossRefGoogle Scholar
  61. [61]
    Abdullah, A R Seadawy and J Wang Brazilian Journal of Physics 49 67 (2019)Google Scholar
  62. [62]
    J Gu, Y Zhang and H Dong Computer Math. with Applications 76 1408 (2018)CrossRefGoogle Scholar

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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