Conservation law and exact solutions for ion acoustic waves in a magnetized quantum plasma

  • Authors

    • Omar El-Kalaawy Beni-Suef University
    • Rafat Ibrahim Beni-Suef University
    • Lamyaa Sadek Beni-Suef University
    2016-06-22
    https://doi.org/10.14419/ijamr.v5i3.6042
  • Head-on collision. Ion- acoustic solitary waves. Magnetized quantum plasma. PLK method. Direct algebraic method. KdV and mKdV equations

  • The head on collision of ion- acoustic solitary waves (IASWs) in a magnetized plasma are considered. The two- sides Korteweg-de Vries (KdV) equations in generic case as well as the two- sides modified Korteweg-de Vries (mKdV) equations in a special case are obtained.

    The analytical phase shifts and the trajectories after the Head-on collisions of two IASWs in a three species quantum plasma are derived by using the extended version of Poincare-Lighthill-Kuo (PLK) method for both the situations. The conservation laws for KdV and mKdV equations are obtained. By applying the extended direct algebraic method, we found the traveling wave solutions for the two-sides KdV and mKdV equations.

  • References

    1. [1] Y.Hase, S. Watanabe, H. Tanaca, Cylindrical ion acoustic soliton in plasma with negative ion. J. Phys. Soc. Jpn. 54, (1985), pp. 4115-4125

      [2] W.S. Duan, X.R. Hong, Y.R. Shi,J.A. Sun, Envelop solitons in dusty plasmas for warm dust. Chaos Soliton & Fractals16, (2003), pp. 767-777

      [3] A. A. Mamun, P.K. Shukla, Cylindrical and spherical dust ionacoustic solitary waves. Phys. Plasmas 9, (2002), pp. 1468-1470

      [4] M.M. Waleed, Dust ion acoustic solitons and shocks in dusty plasmas. Chaos Soliton & Fractals 28, (2006), pp. 994-999

      [5] P.K. Shukla,A. A. Mamun, Introduction to Dusty Plasma Physics ( Bristol U K: Inst. Phys. Publ.) (2002).

      [6] P.K. Shukla, V.P. Silin, Dust ion acoustic wave. Phys. Scr. 45, (1992), pp. 508

      [7] N.N. Rao, P.K. Shukla,M. Yu, Dust-acoustic waves in dusty plasmas. Planet Space Sci. 38, (1990), pp. 543-546

      [8] A. Shah, R. Saeed, Nonlinear Korteweg-de Vries-Burger equation for ion-acoustic shock waves in the presence of kappa distributed electrons and positrons. Plasma Phys. Control. Fusion 53, (2011), pp. 095006-095016

      [9] S. Ghosh, R. Bharuthram, Ion acoustic solitons and double layers in electron-positron-ion plasmas with dust particulates. Astrophys. Space Sci. 314, (2008), pp. 121-127

      [10] A. Barkan, R.L. Merlino, N.D. Angelo, Experiments on ion acoustic waves in dusty plasmas. Planet. Space Sci. 44, (1996), pp. 239-242

      [11] P. Chatterjee, U.N. Ghosh, Head-on collision of ion acoustic solitary waves in electron-positron-ion plasma with superthermal electrons and positrons. Eur. Phys. J. D 64, (2011), pp. 413-417

      [12] P. Chatterjee, K. Roy, U.N. Ghosh, S.V. Muniandy, B. Wong, B. Sahu, Head-on collision of ion acoustic solitary waves in an electronpositronion plasma with superthermal electrons. Phys. Plasmas 17, (2010), pp. 122314-122319

      [13] S.K. El-Labany, E.F. El-Shamy, R. Sabry, M. Shokry. Head on collision of dust-acoustic solitary waves in an adiabatic hot dusty plasma with external oblique magnetic _eld and twotemperature ions. Astrophys. Space Sci. 325, (2010), pp. 201-207

      [14] E.F. El-Shamy, Head-on collision of ion thermal solitary waves in pair-ion plasmas containing charged dust impurities. Eur. Phys. J. D 56, (2010), pp. 73-77

      [15] E.F. El-Shamy, W.M. Moslem, P.K. Shukl, Head-on collision of ion-acoustic solitary waves in a ThomasFermi plasma containing degenerate electrons and positrons. Phys. Lett. A 374, (2009), pp. 290-293

      [16] M.A. Khaled, On the head-on collision between two ion acoustic solitary waves in a weakly relativistic plasma containing nonextensive electrons and positrons. Astrophys. Space Sci. 350, (2014), pp. 607-614

      [17] Y.N. Nejoh, Propagation of ion-acoustic solitary waves in a relativistic electron-positron-ion plasma. Phys. Plasmas. 3,

      (1996), pp. 1447-1451

      [18] R.S. Tiwari, C.A. Kaushi, M.K. Mishra, Effects of positron density and temperature on ion acoustic dressed solitons in an electronpositronion plasma. Phys. Lett. A 365, (2007), p. 335-340

      [19] R. Saeed, A. Shah, Nonlinear Kortewegde VriesBurger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions. Phys. Plasmas. 17, (2010), pp. 032308-032315

      [20] F. Haas, L.G. Gareia, J. Goedert, G. Manfredi, Quantum ion-acoustic waves. Phys.Plasmas. 10, 3858 (2003) pp. 3858-3866

      [21] S. Ali, P.K. Shucla, Dust acoustic solitary waves in a quantum plasma. Phys. Plasmas. 13, (2006), pp. 022313-022318

      [22] P.K. Shukla, B. Eliasson, Formation and Dynamics of Dark Solitons and Vortices in Quantum Electron Plasmas. Phys. Rev. Lett. 96, (2006), pp. 245001-245004

      [23] S. Ali, W.M. Moslem, P.K. Shukla, R. Schlickeiser, Linear and nonlinear ion-acoustic waves in an unmagnetized electron-positron-ion quantum plasma. Phys. Plasmas. 14, (2007a), pp. 082307-082314

      [24] P. Chatterjee, K. Roy, G. Mondel, S.V. Muniandy, S.L. Yap, Dressed soliton in quantum dusty pair-ion plasma. Phys. Plasmas. 16 (2009), pp. 22106-22111

      [25] A. Rasheed, G. Murtaza, N.L. Tsintsadze, Nonlinear structure of ion-acoustic waves in completely degenerate electron-positron and ion plasma. Phys. Rev. E. 82, (2010), pp. 016403-016408

      [26] N.J. Zabusky, M.D. Kruskal, Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States. Phys. Rev.Lett. 15, (1965), pp. 240-243

      [27] M.A. Moghanjoughi, N.A. KhosroShahi, Propagation and oblique collision of electron-acoustic solitons in two-electron-populated quantum plasmas. Pramana J. Phys. 77(2), (2011), pp. 369-382

      [28] H.J. Ning, S.G. Hua, L.Z. Lai, Yi,L.S. Graphene Oxide as Carbon Source for Controlled Growth of Carbon Nanowires. Chin. Phys. B 20, (2011) pp. 025202-025208

      [29] M.K. Ghorui, P. Catterjee, R. Roychoudhury, Interaction during face to face collision between nonlinear electron acoustic solitary waves in quantum plasma. Indian J.phys. 87, (2013), pp. 77-82

      [30] S. Kundu, P. Chatterjee and U. N. Ghosh Astrophys. Head on collision of dust acoustic solitary waves with variable dust charge and two temperature ions in an unmagnetized plasma. Space Sci. 340, (2012), pp. 87-92

      [31] Chatterjee,P., Ghorui, M.K., Wong, C.S. Head-on collision of dust-ion-acoustic soliton in quantum pair-ion plasma. Phys. Plasmas. 18, (2011), pp. 103710- 103716

      [32] J.N. Han, S.C., X.X. Yang, W.S. Duan, Propagation and interaction of ion-Acoustic solitary waves in a two-dimensional plasma consisting of isothermal electrons and hot ions. Eur. Phys. J.D 47, (2008), pp. 197-204

      [33] Hirota, R.: Direct Methods in Soliton Theory. Springer, Berlin (2004)

      [34] C. Rogers and W.E. Shadwisk, Backlund transformations and their applications, Academic Press, New York, (1982).

      [35] 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.

      [36] M.J. Abowitz, P.A. Clarkson, Soliton, Nonlinear evolution equations and inverse scattering. Cambridge University Press (1991).

      [37] J. Weiss, The Painleve property for partial differential equations. II: Backlund transformation, Lax pairs, and the Schwarzian derivative, Journal Mathematical Physics, Vol.24, (1983), pp.1405-1413.

      [38] O. H. EL-Kalaawy and R. B. Aldenari, Painleve analysis, auto-Backlund transformation, and new exact solutions for Schamel and Schamel-Korteweg-de Vries-Burger equations in dust ion-acoustic waves plasma. Physics of Plasmas 21, (2014), pp. 092308-092322

      [39] O. H. EL-Kalaawy and R. B. Aldenari, Painleve analysis, Auto-Backlund transformation and new exact solutions for improved modi_ed KdV equation, International Journal of Applied Mathematical Research, 3 (3) (2014), pp. 265-272

      [40] M.L. Wang, Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213, (5-6) (1996), pp. 279-287

      [41] 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.

      [42] 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.

      [43] 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.

      [44] Y.T. Gao,and . Tian, Cylindrical Kadomtsev-Petviashvili model, nebulons and symbolic computation for cosmic dust ion-acoustic waves, Phys. Lett. A 349, (2006), pp. 314-319

      [45] Y.T. Gao, and B. Tian, Spherical Kadomtsev-Petviashvili equation and nebulons for dust ion acoustic waves with symbolic computation. Phys. Lett. A 361, (2007), pp.523-528

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  • How to Cite

    El-Kalaawy, O., Ibrahim, R., & Sadek, L. (2016). Conservation law and exact solutions for ion acoustic waves in a magnetized quantum plasma. International Journal of Applied Mathematical Research, 5(3), 138-145. https://doi.org/10.14419/ijamr.v5i3.6042