Rouge wave solutions of a nonlinear pseudo-parabolic physical model through the advance exponential expansion method

  • Authors

    • Md. Habibul Bashar European University of Bangladesh
    • Md. Mamunur Roshid pabna university of science & technology
    2020-04-28
    https://doi.org/10.14419/ijpr.v8i1.30475
  • Oskolkov Equation, The Advance -Expansion Method, Nonlinear Pseudo-Parabolic Physical Models, Bright and Dark Rouge Wave, Kinky Periodic Wave, Breather Wave.
  • Abstract

    In this work, we decide the proliferation of nonlinear voyaging wave answers for the dominant nonlinear pseudo-parabolic physical model through the (1+1)-dimensional Oskolkov equation. With the assistance of the advance -expansion strategy compilation of disguise adaptation an innovative version of interacting analytical solutions regarding, hyperbolic and trigonometric function with some refreshing parameters. We analyze the behavior of these solutions of Oskolkov equations for the specific values of the reared parameters such as rouge wave, multi solution, breather wave bell and kink shape etc. The dynamics nonlinear wave solution is examined and demonstrated in 3-D and 2-D plots with specific values of the perplexing parameters are plotted. The advance -expansion method solid treatment for looking through fundamental nonlinear waves that advance assortment of dynamic models emerges in engineering fields.

     

     

  • References

    1. [1] E. Yasar, Y. Yıldırım and A. R. Adem, “Perturbed optical solitons with spatio-temporal dispersion in (2 + 1)-dimensions by extended Kudryashov methodâ€, Optik, 158, (2018), 1–14. https://doi.org/10.1016/j.ijleo.2017.11.205.

      [2] H. O. Roshid, M. M. Roshid, N. Rahman and M. R. Pervin, “New solitary wave in shallow water, plasma and ion acoustic plasma via the GZK-BBM equation and the RLW equationâ€, Propulsion and Power Research, 6(1), (2017), 49–57. https://doi.org/10.1016/j.jppr.2017.02.002.

      [3] H. O. Roshid, M. F. Hoque and M. A. Akbar, “New extended (G’/G)-expansion method for traveling wave solutions of nonlinear partial differential equations (NPDEs) in mathematical physicsâ€, Italian. J. Pure Appl. Math., 33, (2014), 175-190.

      [4] L. L. Feng and T.T. Zhang, “Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrodinger equationâ€, Appl. Math. Lett., 78, (2018), 133-140. https://doi.org/10.1016/j.aml.2017.11.011.

      [5] X. Shuwei and H. Jingsong, “The rogue wave and breather solution of the Gerdjikov-Ivanov equationâ€, Journal of Mathematical Physics, 53, (2012). https://doi.org/10.1063/1.4726510.

      [6] A. Biswas, M. Mirzazadeh, M. Eslami, Q. Zhou, A. Bhrawy amd M. Belic, “Optical solitons in nano-fibers with spatio-temporal dispersion by trial solution methodâ€, Optik, 127, (18), (2016), 7250–7257. https://doi.org/10.1016/j.ijleo.2016.05.052.

      [7] J. M. Heris and I. Zamanpour, “Analytical treatment of the Coupled Higgs Equation and the Maccari System via Exp-Function Methodâ€, 33, (2013), 203-216.

      [8] Y. M. Zhao, “New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using the Multiple Simplest Equation Methodâ€, Journal of Applied Mathematics, (2014), 1-13. https://doi.org/10.1155/2014/848069.

      [9] M. Alquran, “Bright and dark soliton solutions to the Ostrovsky-Benjamin-Bona-Mahony (OS-BBM) equationâ€, J. Math. Comput. Sci., 2, (2012), 15-22.

      [10] T. A. Nofal, “Simple equation method for nonlinear partial differential equations and its applicationsâ€, Journal of the Egyptian Mathematical Society, (2015). https://doi.org/10.1016/j.joems.2015.05.006.

      [11] S. Bilige, T. Chaolu, and X. Wang, “Application of the extended simplest equation method to the coupled Schrödinger-Boussinesq equationâ€, Applied Mathematics and Computation, 224, (2013), 517–523. https://doi.org/10.1016/j.amc.2013.08.083.

      [12] N. A. Kudryashov, “Simplest equation method to look for exact solutions of nonlinear differential equationsâ€, Chaos, Solitons & Fractals, 24 (5), (2005), 1217–1231. https://doi.org/10.1016/j.chaos.2004.09.109.

      [13] N. Taghizadeha, M. Mirzazadeha, M. Rahimianb and M. Akbaria, “Application of the simplest equation method to some time-fractional partial differential equationsâ€, Ain Shams Engineering Journal, 4 (4), (2013), 897-902. https://doi.org/10.1016/j.asej.2013.01.006.

      [14] M. Roshid and H. Bashar “Breather Wave and Kinky Periodic Wave Solutions of One-Dimensional Oskolkov Equationâ€, Mathematical Modelling of Engineering Problems, Vol. 6, No. 3, PP.460-466, https://doi.org/10.18280/mmep.060319.

      [15] M. M. Roshid and H.O. Roshid, “Exact and explicit traveling wave solutions to two nonlinear evolution equations which describe incompressible viscoelastic Kelvin-Voigt fluidâ€, Heliyon,4, (2018). https://doi.org/10.1016/j.heliyon.2018.e00756.

      [16] O. F. Gozukızıl and S. Akcagıl, “The tanh-coth method for some nonlinear pseudoparabolic equations with exact solutionsâ€, Advances in Difference Equations, 143, (2013). https://doi.org/10.1186/1687-1847-2013-143.

      [17] A. K. Turgut, T. Aydemir, A. Saha and A. H. Kara, “Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbationâ€, Pramana – J. Phys., (2018), 78-90. https://doi.org/10.1007/s12043-018-1564-7.

      [18] G. A. Sviridyuk and A. S. Shipilov, “On the Stability of Solutions of the Oskolkov Equations on a Graphâ€, Differential Equations, 46(5), (2010),742–747. https://doi.org/10.1134/S0012266110050137.

      [19] S. Akcagil, T. Aydemir and O. F. Gozukizil, “Exact travelling wave solutions of nonlinear pseudoparabolic equations by using the Expansion Methodâ€, NTMSCI, 4(4), (2016), 51-66. https://doi.org/10.20852/ntmsci.2016422120.

      [20] G. A. Sviridyuk and M. M. Yakupov, “The phase space of Cauchy-Dirichlet problem for a non-classical equationâ€, Differ. Uravn. (Minsk), 39(11), (2003), 1556-1561. https://doi.org/10.1023/B:DIEQ.0000019357.68736.15.

      [21] M. M. Rahhman, A. Aktar and K. C. Roy, “Analytical Solutions of Nonlinear Coupled Schrodinger–KdV Equation via Advance Exponential Expansionâ€, American Journal of Mathematical and Computer Modelling, 3(3), (2018), 46-51. https://doi.org/10.11648/j.ajmcm.20180303.11.

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  • How to Cite

    Habibul Bashar, M., & Mamunur Roshid, M. (2020). Rouge wave solutions of a nonlinear pseudo-parabolic physical model through the advance exponential expansion method. International Journal of Physical Research, 8(1), 1-7. https://doi.org/10.14419/ijpr.v8i1.30475

    Received date: 2020-02-28

    Accepted date: 2020-04-11

    Published date: 2020-04-28