Symmetry Analysis and Solitary Wave Solutions of Nonlinear Ion-Acoustic Waves Equation

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M.H.M. Moussa, A.A. Gaber, Symmetry Analysis and Solitary Wave Solutions of Nonlinear Ion-Acoustic Waves Equation, Int. J. Anal. Appl., 18 (3) (2020), 448-460.

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M.H.M. Moussa, A.A. Gaber

Abstract

The problem of nonlinear ion-acoustic waves equation in a magnetized plasma, known as Zakharov-Kuznetsov equation, is investigated by using symmetry analysis. The carryover of the symmetry analysis has led to certain similarity reductions of this equation. Furthermore, exact solutions of similarity reductions are obtained by modified Exp-Function method with computational symbolic. Some figures are obtained to show the properties of the solutions.

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References

  1. Abdullahi Rashid Adem, Symbolic computation on exact solutions of a coupled Kadomtsev Petviashvili equation: Lie symmetry analysis and extended tanh method, Comput. Math. Appl. 74 (8) (2017), 1897-1902.
  2. Anupma Bansal, Anjan Biswas, Qin Zhou, M.M. Babatin, Lie symmetry analysis for cubic-quartic nonlinear Schr ¨odinger's equation, Optik, 169 (2018), 12-15.
  3. E.M.E.Zayed, K.A.E.Alurrfi, Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrodinger-type equations, Appl. Math. Comput. 289 (2016), 111-131.
  4. M.A.Abdou, A.A.Soliman, On completely integrable coupled Burgers and coupled Korteweg-deVriessystems, Appl. Math Lett. 25 (2012), 2052-2057.
  5. E.M.E.Zayed, Abdul-GhaniAl-Nowehy, Exact solutions and optical soliton solutions for the (2 + 1)-dimensional hyperbolic nonlinear Schrodinger equation, Optik, 127 (12) (2016), 4970-4983.
  6. L.V. Ovsiannikov, Group analysis of differential equations. Moscow: Nauka; 1978.
  7. Olver PJ. Application of lie groups to differential equations. Springer-Verlag; 1986.
  8. Ibragimov NH, editor. CRC handbook of lie group analysis of differential equations, vols. I, II, III; 1994
  9. G.W. Bluman, S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
  10. Huaitang Chen, Huicheng Yin, A note on the elliptic equation method, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), 547-553.
  11. V.E. Zakharov, E.A. Kuznetsov, On three-dimensional solitons. Sov. Phys. JETP. 39 (1974), 285-286.
  12. H.A. Biagioni, F. Linares, Well-posedness Results for the Modified Zakharov-Kuznetsov Equation. In: Lupo D., Pagani C.D., Ruf B. (eds) Nonlinear Equations: Methods, Models and Applications. Progress in Nonlinear Differential Equations and Their Applications, Birkh ¨auser, Basel, 54 (2003), 181-189.
  13. A. A. El-Satar, Similarity Reductions and New Exact Solutions for B-Family Equations, Amer. J. Math. Stat. 2 (3) (2012), 40-43.
  14. M.H.M. Moussa, Similarity Reductions to nonlinear partial differential equation to physical phenomena represented by the Zakharov-Kuznetsovequation, Inter. J. Eng. Sci. 39 (2001), 1565-1575.
  15. T. Ozer, New exact solutions to the CDF equations, Chaos Solitons Fractals, 39 (2007), 1371-1385
  16. M.H.M. Moussa, Similarities, symmetries, singularities and exact solutions for nonlinear system, Ph. D. Thesis, IIT, Delhi, 1991.
  17. A.H. Khater, M.H.M. Moussa, S.F. Abdul-Aziz and H.M.S. Khidr, On the similarity solutions of the variable-coefficient semi-linear hyperbolic equation uxt= α (t) f (u) via a symmetry method, IL Nuovo. Cimento B, 116 (2001), 889-906.
  18. A.H. Khater, W. Malfiet, M.H.M. Moussa, S.F. Abdul-Aziz, On the similarity solutions of the Calogero-Degasperis-Fokas modified KdV equation via symmetry method, J. Phys. Soc. Japan, 72 (10) (2003), 2523-2529.
  19. M.F. El-Sayed, G.M. Moatimid, M.H.M. Moussa, RM El-Shiekh, New exact solutions for the classical Drinfel'd-SokolovWilson equation using the first integral method, Int. J. Adv. Appl. Math. Mech. 1(4) (2014), 52-60.
  20. M. H. M. Moussa, Rehab M. El Shikh, Similarity Reduction and similarity solutions of Zabolotskay-Khoklov equation with a dissipative term via symmetry method, Physica A, 371 (2006), 325-335.
  21. A. A. El-Satar, Symmetry group analysis and similarity solutions for the (2+ 1)-dimensional coupled Burger's system, Math. Method Appl. Sci. 37 (8) (2014), 1113-1120.
  22. A.A. El-Satar, A study of integrability and symmetry for the (p + 1)th Boltzmann equation via Painlev ´e analysis and Lie-group method, Math. Method Appl. Sci. 38 (17) (2015), 3670-3677.
  23. Abd El-Halim Ebaid, Generalization of He's Exp-Function Method and New Exact Solutions for Burgers Equation, Z. Naturforsch. A, 64 (2009), 604-608.
  24. Abd El-Halim Ebaid, An improvement on the Exp-function method when balancing the highest order linear and nonlinear terms, J. Math. Anal. Appl. 392 (2012), 1-5.
  25. A. A. Gaber and et., The generalized version of Kudryashov method for nonlinear space-time fractional partial differential equations of Burgers type, Nonlinear Dyn. 95 (2019), 361-368.