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New travelling wave solutions for plasma model of extended K–dV equation

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Abstract

In this paper we aims to obtain new exact and analytical solutions for extended Korteweg–de Vries (K–dV) equation by using of new modified method named Riccati equation method. We introduce the extended K–dV equation with help of the reductive perturbation method, which admits a double layer structure in current plasma model. The obtained solutions are expressed by the hyperbolic, trigonometric and rational functions. Our calculations show that, considered method is straightforward to solve nonlinear partial differential equations. This method is not only powerful mathematical tool for generating more solutions of nonlinear partial differential equations but also can be applied to nonlinear partial differential equations.

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References

  1. Fan, E.: Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277(4–5), 212–218 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Fan, E.: Travelling wave solutions for generalized Hirota–Satsuma coupled KdV systems. Z Naturforsch A 56, 312–318 (2001)

    Article  Google Scholar 

  3. Wazwaz, A.M.: A sine-cosine method for handing nonlinear wave equations. Math. Comput. 40(5–6), 499–508 (2004)

    MATH  Google Scholar 

  4. Chen, H.-T., Zhang, H.-Q.: New double periodic and multiple soliton solutions of the generalized (2 + 1)-dimensional Boussinesq equation. Chaos. Soliton. Fract. 20, 765–769 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ali, A.H.A., Soliman, A.A., Raslan, K.R.: Soliton solution for nonlinear partial differential equations by cosine-function method. Phys. Lett. A 368, 299–304 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hosseini, K., Mayeli, P., Ansari, R.: Modified Kudryashov method for solving the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities. Opt. Int. J. Light Electron Opt. 130, 737–742 (2017)

    Article  Google Scholar 

  7. Hosseini, K., & Ansari, R. (2017). New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method. In: Waves in Random and Complex Media, pp. 1–9

  8. Hosseini, K., Bekir, A., Ansari, R.: New exact solutions of the conformable time-fractional Cahn–Allen and Cahn–Hilliard equations using the modified Kudryashov method. Opt. Int. J. Light Electron Opt. 132, 203–209 (2017)

    Article  Google Scholar 

  9. Aminikhah, H., Sheikhani, A.R., Rezazadeh, H.: Sub-equation method for the fractional regularized long-wave equations with conformable fractional derivatives. Sci. Iran. Trans. B Mech. Eng. 23(3), 1048 (2016)

    Google Scholar 

  10. Akbulut, A., Kaplan, M.: Auxiliary equation method for time-fractional differential equations with conformable derivative. Comput. Math. Appl. 75(3), 876–882 (2018)

    Article  MathSciNet  Google Scholar 

  11. Ekici, M., Mirzazadeh, M., Eslami, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives. Opt. Int. J. Light Electron Opt. 127(22), 10659–10669 (2016)

    Article  Google Scholar 

  12. Kurt, A., Tasbozan, O., Cenesiz, Y., Baleanu, D.: New exact solutions for some nonlinear conformable PDEs using Exp-function method. In: International Conference on Applied Mathematics and Analysis in Memory of Gusein Sh. Guseinov. Atilim University Ankara, Turkey (2016)

  13. Bibi, S., Mohyud-Din, S.T., Khan, U., Ahmed, N.: Khater method for nonlinear Sharma Tasso–Olever (STO) equation of fractional order. Results Phys. 7, 4440–4450 (2017)

    Article  Google Scholar 

  14. Zuo, J.M., Zhang, Y.M.: Application of the (G′/G)-expansion method to solve coupled MKdV equations and coupled Hirota–Satsuma coupled KdV equations. Appl. Math. Comput. 217(12), 5936–5941 (2011)

    MathSciNet  MATH  Google Scholar 

  15. Zhang, J., Jiang, F., Zhao, X.: An improved (G′/G)-expansion method for solving nonlinear evolution equations. Int. J. Comput. Math. 87(8), 1716–1725 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hafez, M.G., Akbar, M.A.: New exact traveling wave solutions to the (1 + 1)-dimensional Klein–Gordon–Zakharov equation for wave propagation in plasma using the exp (− Φ (ξ))-expansion method. Propuls. Power Res. 4(1), 31–39 (2015)

    Article  Google Scholar 

  17. El-Wakil, S.A., Abdou, M.A.: New exact travelling wave solutions using modified extended tanh-function method. Chaos Solitons Fract. 31(4), 840–852 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Formisano, V., Moreno, G., Palmiotto, F., Hedgecock, P.C.: Solar wind interaction with the Earth's magnetic field: 1. Magnetosheath. J. Geophys. Res. 78 (19), 3714–3730 (1973)

    Article  Google Scholar 

  19. Leubner, M.P.: A nonextensive entropy approach to kappa-distributions. Astrophys. Space Sci. 282, 573–579 (2002)

    Article  Google Scholar 

  20. Pierrard, V., Lazar, M.: Kappa distributions: theory and applications in space plasmas. Sol. Phys. 267, 153–174 (2010)

    Article  Google Scholar 

  21. Liu, J.-G., Tian, Y., Zeng, Z.-F.: New exact periodic solitary-wave solutions for the new (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation in multi-temperature electron plasmas. AIP Adv. 7, 105013 (2017)

    Article  Google Scholar 

  22. Chen, J.-Y., Kincaid, D.R., Lin, B.-R.: New non-traveling wave solutions for the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Appl. Math. Lett. 79, 162–168 (2018)

    Article  MathSciNet  Google Scholar 

  23. Liu, J.-G., Tian, Y.: New double-periodic soliton solutions for the (2 + 1)-dimensional breaking soliton equation. Commun. Theor. Phys. 69(5), 585–597 (2018)

    Article  MATH  Google Scholar 

  24. Liu, J.-G., He, Y.: New periodic solitary wave solutions for the (3 + 1)-dimensional generalized shallow water equation. Nonlinear Dyn. 90(1), 363–369 (2017)

    Article  MathSciNet  Google Scholar 

  25. Liu, J.-G., Jian-Qiang, D., Zeng, Z.-F., Nie, B.: New three-wave solutions for the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Nonlinear Dyn. 88(1), 655–661 (2017)

    Article  MathSciNet  Google Scholar 

  26. Liu, J.-G., He, Y.: Abundant lump and lump-kink solutions for the new (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation. Nonlinear Dyn. 92, 1103–1108 (2018)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad, Iran

    Ahmad Neirameh

  2. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    Mostafa Eslami

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  1. Ahmad Neirameh
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  2. Mostafa Eslami
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Correspondence to Ahmad Neirameh.

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Neirameh, A., Eslami, M. New travelling wave solutions for plasma model of extended K–dV equation. Afr. Mat. 30, 335–344 (2019). https://doi.org/10.1007/s13370-018-00651-2

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  • DOI: https://doi.org/10.1007/s13370-018-00651-2

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