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Nonlinear dust acoustic travelling waves in dusty plasmas due to dust charge fluctuations

  • Asit Saha (a1) (a2), Prasanta Chatterjee (a2) and Nikhil Pal (a2)

Abstract

Dust acoustic solitary waves, blow-up solitary waves and periodic waves have been investigated in unmagnetized dusty plasmas with Maxwell-distributed electrons and ions, considering dust charge fluctuations using the bifurcation theory of planar dynamical systems. The basic equations are transformed to an ordinary differential equation involving the electrostatic potential. Applying the bifurcation theory of planar dynamical systems, we have established the existence of solitary, blow-up solitary and periodic waves. Four exact solutions of the solitary, blow-up solitary and periodic waves are derived depending on the physical parameters. Regarding the solitary, blow-up solitary and periodic waves, we have presented the combined effects of the density ratio of electrons and ions ( ${\it\alpha}$ ), the temperature ratio of electrons and ions $({\it\beta})$ and the speed of the travelling wave ( $v$ ) on the characteristics of dust acoustic solitary, blow-up solitary and periodic waves.

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Email address for correspondence: asit_saha123@rediffmail.com

References

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Asgari, H., Muniandy, S. V. & Wong, C. S. 2011 The role of dust charging frequency in the linear and nonlinear propagation of dust acoustic waves. Wave Motion 48, 268274.
Barkan, A., Merlino, R. L. & D’Angelo, N. 1995 Laboratory observation of the dust-acoustic wave mode. Phys. Plasmas 2, 3563.
Barkan, A., Merlino, R. L. & D’Angelo, N. 1996 Experiments on ion-acoustic waves in dusty plasmas. Planet. Space Sci. 44, 239242.
Chatterjee, P. 2004 Speed and shape of solitary waves in two-electron plasmas with relativistic warm ions. Z. Naturforsch. A 59, 353.
Chatterjee, P. & Das, B. 2004a Speed and shape of solitary waves in non-isothermal plasma with warm ions. Indian J. Phys. 78B, 223.
Chatterjee, P. & Das, B. 2004b Effect of electron inertia on the speed and shape of ion-acoustic solitary waves in plasma. Phys. Plasmas 11, 3616.
Chatterjee, P. & Roychoudhury, R. 1994 Effect of ion temperature on large-amplitude ion-acoustic solitary waves in relativistic plasma. Phys. Plasmas 1, 2148.
D’Angelo, N. 1990 Low-frequency electrostatic waves in dusty plasmas. Planet. Space Sci. 38, 11431146.
D’Angelo, N. 1995 Coulomb solids and low-frequency fluctuations in RF dusty plasmas. J. Phys. D 28, 1009.
Duan, W. S., Lu, K. P. & Zhao, J. B. 2001 Hot dust acoustic solitary waves in dust plasma with variable dust charge. Chin. Phys. Lett. 18, 1088.
El-Labany, S. K. & El-Taibany, W. F. 2004 Effect of dust-charge variation on dust acoustic solitary waves in a dusty plasma with trapped electrons. J. Plasma Phys. 70, 6987.
El-Labany, S. K., El-Taibany, W. F., El-Bedwehy, N. A. & El-Fayoumy, M. M. 2011 Arbitrary amplitude dust acoustic solitary waves in a dusty plasma with an ion beam. Eur. Phys. J. D 64, 375.
Goertz, C. K. 1989 Dusty plasmas in the solar system. Rev. Geophys. 27, 271292.
Guckenheimer, J. & Holmes, P. J. 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer.
Johnston, C. R. & Epstein, M. 2000 On the exact amplitude, speed and shape of ion-acoustic waves. Phys. Plasmas 7, 906.
Kourakis, I. & Shukla, P. K. 2004 Lagrangian description of nonlinear dust-ion acoustic waves in dusty plasmas. Eur. Phys. J. D 30, 97103.
Maitra, S. & Roychoudhury, R. 2003 Speed and shape of dust acoustic solitary waves. Phys. Plasmas 10, 2230.
Malfliet, W. & Wieers, E. 1996 The theory of nonlinear ion-acoustic waves revisited. J. Plasma Phys. 56, 441450.
Melandso, F. 1996 Lattice waves in dust plasma crystals. Phys. Plasmas 3, 3890.
Mendis, D. A. 2002 Progress in the study of dusty plasmas. Plasma Sources Sci. Technol. 11, A219.
Nejoh, Y. N. 1997 The dust charging effect on electrostatic ion waves in a dusty plasma with trapped electrons. Phys. Plasmas 4, 2813.
Nakamura, Y., Bailung, H. & Shukla, P. K. 1999 Observation of ion-acoustic shocks in a dusty plasma. Phys. Rev. Lett. 83, 1602.
Rao, N. N. & Shukla, P. K. 1994 Nonlinear dust-acoustic waves with dust charge fluctuations. Planet. Space Sci. 42 (3), 221225.
Rao, N. N., Shukla, P. K. & Yu, M. Y. 1990 Dust-acoustic waves in dusty plasmas. Planet. Space Sci. 38, 543546.
Saha, A. 2012 Bifurcation of travelling wave solutions for the generalized KP-MEW equations. Commun. Nonlinear Sci. Numer. Simul. 17, 35393551.
Saha, A. & Chatterjee, P. 2014a Bifurcations of electron acoustic traveling waves in an unmagnetized quantum plasma with cold and hot electrons. Astrophys. Space Sci. 349, 239244.
Saha, A. & Chatterjee, P. 2014b Bifurcations of ion acoustic solitary waves and periodic waves in an unmagnetized plasma with kappa distributed multi-temperature electrons. Astrophys. Space Sci. 350, 631636.
Saha, A. & Chatterjee, P. 2014c Bifurcations of ion acoustic solitary and periodic waves in an electron–positron–ion plasma through non-perturbative approach. J. Plasma Phys. 80, 553563.
Saha, A. & Chatterjee, P. 2014d Bifurcations of dust acoustic solitary waves and periodic waves in an unmagnetized plasma with nonextensive ions. Astrophys. Space Sci. 351, 533537.
Saha, A. & Chatterjee, P. 2014e New analytical solutions for dust acoustic solitary and periodic waves in an unmagnetized dusty plasma with kappa distributed electrons and ions. Phys. Plasmas 21, 022111.
Samanta, U. K., Saha, A. & Chatterjee, P. 2013a Bifurcations of nonlinear ion acoustic travelling waves in the frame of a Zakharov–Kuznetsov equation in magnetized plasma with a kappa distributed electron. Phys. Plasmas 20, 052111.
Samanta, U. K., Saha, A. & Chatterjee, P. 2013b Bifurcations of dust ion acoustic travelling waves in a magnetized dusty plasma with a $q$ -nonextensive electron velocity distribution. Phys. Plasmas 20, 022111.
Samanta, U. K., Saha, A. & Chatterjee, P. 2013c Bifurcations of dust ion acoustic travelling waves in a magnetized quantum dusty plasma. Astrophys. Space Sci. 347, 293298.
Selwyn, G. S. 1993 A phenomenlogical study of particulates in plasma tools and processes. Japan. J. Appl. Phys. 32, 3068.
Shukla, P. K. & Silin, V. P. 1992 Dust ion-acoustic wave. Phys. Scr. 45, 508.
Shukla, P. K. & Varma, R. K. 1993 Convective cells in nonuniform dusty plasmas. Phys. Fluids B 5, 236.
Shukla, P. K., Yu, M. Y. & Bharuthram, R. 1991 Linear and nonlinear dust drift waves. J. Geophys. Res. 96, 2134321346.
Thomas, H., Morfill, G. E. & Dammel, V. 1994 Plasma crystal: Coulomb crystallization in a dusty plasma. Phys Rev. Lett. 73, 652.
Tribeche, M. & Bacha, M. 2010 Nonlinear dust acoustic waves in a charge varying dusty plasma with suprathermal electrons. Phys. Plasmas 17, 073701.
Tribeche, M. & Zerguini, T. H. 2004 Small amplitude Bernstein–Greene–Kruskal solitary waves in a thermal charge-varying dusty plasma. Phys. Plasmas 11, 4115.
Verheest, F. 2000 Waves in Dusty Space Plasmas. Kluwer.
Verheest, F., Hellberg, M. A. & Kourakis, I. 2008 Acoustic solitary waves in dusty and/or multi-ion plasmas with cold, adiabatic, and hot constituents. Phys. Plasmas 15, 112309.
Watanabe, S. & Jiang, B. 1993 Higher-order solution of an ion-acoustic solitary wave in a plasma. Phys. Fluids B 5, 409.
Xie, B., He, K. & Huang, Z. 1999 Dust-acoustic solitary waves and double layers in dusty plasma with variable dust charge and two-temperature ions. Phys. Plasmas 6, 3808.
Xue, J. K. 2003 A spherical KP equation for dust acoustic waves. Phys. Lett. A 314, 479483.
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Nonlinear dust acoustic travelling waves in dusty plasmas due to dust charge fluctuations

  • Asit Saha (a1) (a2), Prasanta Chatterjee (a2) and Nikhil Pal (a2)

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