Painleve analysis, Auto-Backlund transformation and new exact solutions for improved modied KdV equation

  • Abstract
  • Keywords
  • References
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  • Abstract

    Improved modied Korteweg-de Vries (IMKdV) equation is shown to be non-integrable using Painleve analysis. Exact travelling wave solutions are obtained using auto-Backlund transformation and Linearized transformation.

    Keywords: IMKdV equation; Painleve analysis; extended homogeneous balance method, auto-Backlund transformation, Linearized transformation, and exact solutions.

  • References

    1. M.J. Abowitz, P.A. Clarkson, Soliton, "Nonlinear evolution equations and inverse scattering". Cambridge University Press (1991).
    2. M. Ablowitz, D. Kaup, A. Newell, H. Segur, "The inverse scattering transform-Fourier analysis for nonlinear problems", Studies in Applied Mathematics, Vol.53, (1974), pp.249-315.
    3. K. Konno, M. Wadati, "Simple derivation of Backlund transformation from Riccati form of inverse method", Progress. Theoret. Phys., Vol.53, (1975), pp.1652-1655.
    4. C. Rogers and W.E. Shadwisk," Backlund transformations and their applications," Academic Press, New York, (1982).
    5. M. Wadati, H. Sunukt and K. Konno, "Relationships among inverse method, Backlund transformation and an innite number of conservatioq laws", Progress Theortical Physics, Vol.53, (1975), pp.419-436.
    6. A.H. Khater, M.A. Helal and O.H. El-Kalaawy, "Two new classes of exact solutions for the KdV equation via Backlund transformations", Chaos Solitons Fractals, Vol.8, (1997), pp.1901-1907.
    7. J. Weiss, M. Tabor, and G. Carnevale, The Painleve property for partial dierential equations, Journal of Mathematical Physics, vol.24, No.3, (1983), pp.522-526.
    8. J. Weiss, "The Painleve property for partial dierential equations. II: Backlund transformation, Lax pairs, and theSchwarzian derivative", Journal Mathematical Physics, Vol.24, (1983), pp.1405-1413.
    9. B. Tian, Y.T. Gao, "Truncated Painlev e expansion and a wide-ranging type of generalized variable-coecient Kadomtsev-Petviashvili equations", Physics Letters A, Vol.209, (1995), pp.297-304.
    10. R. Hirota "Exact solution of the Korteweg-de Vries equation for multiple collisions of solutions", Physics Review Letters, Vol.72, (1971), pp.1192-1194.
    11. W. Malfliet, "Solitary wave solutions of nonlinear wave equations", American Journal Physics, Vol.60 (1992), pp. 650-654.
    12. W. Malfliet and W. Hereman "The tanh method: I. Exact solutions of nonlinear evolution and wave equations". Physica Scripta, Vol.54, (1996), pp.563-568.
    13. M. L. Wang,", Solitary wave solutions for variant Boussinesq equations" Physics Letters A, Vol.199, (1995), pp.169-172.
    14. M. L. Wang," Exact solutions for a compound KdV-Burgers equation", Physics Letters A, vol.213, No.5-6, (1996), pp. 279-287.
    15. E. Fan and H. Q. Zhang," New exact solutions to a system of coupled KdV equations", Physics Letters A,Vol.245, (1998), pp.389-392.
    16. A.M. Wazwaz, "The tanh and the sine-cosine methods for the complex modied KdV and the generalized KdV equation", Computional Mathathematical and Application, Vol.49, (2005), pp.1101-1112.
    17. M.A. Abdou, "Further Improved F-expansion and new exact solutions for nonlinear evolution equations" Nonlinear Dynamics, Vol.52, No.3, (2008), pp.277-288.
    18. D.H. Feng and G.X. Luo, "The Improved Fan Sub- equation method and its application to the SK equation", Applied Mathematics and Computation, Vol.215, No.5, (2009), pp.1949-1967.
    19. M. Wang, X. Li and J. Zhang, "The (G0=G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics", Physics Letters A, Vol. 372, No. 4, (2008), pp.417-423.
    20. K. Javidan and H.R. Pakzad,"Obliquely propagating electron acoustic solitons in a magnetized plasma with superthermal electrons" Indian Journal Physics, Vol.87, (2013), pp.83-87.
    21. O.H. El-Kalaawy and R.S. Ibrahimb,"Exact solutions for nonlinear propagation of slow ion acoustic monotonic double layers and a solitary hole in a semirelativistic plasma" Physics of Plasmas , Vol.15, (2008), pp.072303-072307.
    22. O. H. EL-Kalaawy,"Exact soliton solutions for some nonlinear partial dierential equations" Chaos, Solitons & Fractals, Vol.14, (2002), pp.547-552.
    23. Liu Chun-Ping and Zhou Ling,"A new auto-Baacklund transformation and two-soliton solution for (3+1)-dimensional Jimbo-Miwa equation" Communications in Theoretical Physics, Vol.55, (2011), pp.213-216.
    24. Qin Yi, Gao Yi-Tian, Yu Xin and Meng Gao-Qing,"Bell polynomial approach and N-soliton solutions for a coupled KdV-mKdV system " Communications in Theoretical Physics, Vol.58, No.1, (2012) pp.73-77.




Article ID: 2940
DOI: 10.14419/ijamr.v3i3.2940

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