Skip to main content Accessibility help

Ion-acoustic envelope excitations in multispecies plasma with non-thermally distributed electrons



By using the standard reductive perturbation technique, a nonlinear Schrödinger equation is derived to study the stability of finite amplitude ion-acoustic waves in an unmagnetized plasma consisting of warm positive and negative ions and non-thermal electrons. The effect of relative temperature of positive and negative ions, their charge and mass ratios, density ratios and non-thermally distributed electrons on modulational instability of fast and slow ion-acoustic mode is investigated. It is found that these parameters significantly change the domain of modulation instability. Both, envelope and dark solitons appear in different regions of parameter space.



Hide All
Abdullaev, F. K., Bouketir, A., Messikh, A. and Umarov, B. A. 2007 Modulational instability and discrete breathers in the discrete cubic-quintic nonlinear Schrödinger equation. Physica D 232, 5461.
Aggrawal, G. P. 2007 Nonlinear Fibre Optics. San Diego, CA: Academic Press.
Amin, M. R., Morfill, G. E. and Shukla, P. K. 1998 Modulational instability of dust-ion-acoustic waves. Phys. Rev. E 58, 65176523.
Bailung, H., Chutia, J. and Nakamura, Y. 1996 Propagation of solitary ion wavepacket in multi-component plasma with negative ions. Chaos Solitons Fractals 7, 2124.
Bailung, H. and Nakamura, Y. 1993 Observation of modulational instability in a multicomponent plasma with negative ions. J. Plasma Phys. 2, 231242.
Ballav, M. and Chowdhury, A. R. 2007 A generalized nonlinear Schrödinger equation and optical soliton in a gradient index cylindrical media. Chaos Solitons Fractals 31, 794803.
Benjamin, T. B. and Feir, J. E. 1967 The disintegration of wave trains in deep water Part I. J. Fluid Mech. 27, 417430.
Bharuthram, R. 1992 Arbitrary amplitude double layers in a multi-species electron positron plasma. Astrophys Space Sci. 189, 213222.
Bilbault, J. M., Marquie, P. and Michaux, B. 1995 Modulational instability of two counterpropagating waves in an experimental transmission line. Phys. Rev. E 51, 817820.
Cairns, R. A., Mamun, A. A., Bingham, R., Bostrom, R., Dendy, R. O., Nairn, C. M. C. and Shukla, P. K. 1995 Electrostatic solitary structures in nonthermal plasmas. Geophys. Res. Lett. 22, 27092712.
Chhabra, R. S. and Sharma, S. R. 1986 Modulational instability of obliquely modulated ion-acoustic waves in a two ion plasma. Phys Fluids. 29, 128132.
Dauxois, T. and Peyrard, M. 2006 Physics of Solitons. Cambridge, UK: Cambridge University Press.
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. New York and London: Academic Press, pp. 37.
Davydov, A. S. 1985 Solitons in Molecular Systems. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Duan, W. S. 2006 3+1 dimensional envelope waves and its stability in magnetized dusty plasma. Chaos Solitons Fractals 27, 926929.
El-Dib, Y. O. 2000 Instability of parametrically second- and third-subharmonic resonances governed by nonlinear Schrödinger equations with complex coefficients. Chaos Solitons Fractals 11, 17731787.
El-labany, S. K., Krim, M. S. A., El-Warraki, S. A. and El-Taibany, W. F. 2003 Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons. Chin. Phys. Soc. 12, 759764.
El-Shewy, E. K. 2007 Higher order solution of an electron-acoustic solitary waves with nonthermal electrons. Chaos, Solitons Fractals 34, 628638.
Ganapathy, R., Malomed, B. A. and Porsezian, K. 2006 Modulational instability and generation of pulse trains in asymmetric dual-core nonlinear optical fibers. Phys. Lett. A 354, 366372.
Gill, T. S., Bala, P., Kaur, H. and Saini, N. S. 2004 Ion-acoustic solitons and double-layers in a plasma consisting of positive and negative ions with non-thermal electrons. Eur. Phys. J. D 31, 91100.
Gill, T. S., Kaur, H., Bansal, S., Saini, N. S. and Bala, P. 2007 Modulational instability of electron-acoustic waves: an application to auroral zone plasma. Eur. Phys. J. D 41, 151156.
Gill, T. S., Kaur, H. and Saini, N. S. 2006 Small amplitude electron-acoustic solitary waves in a plasma with nonthermal electrons. Chaos, Solitons Fractals 30, 10201024.
Griffiths, S. D., Grimshaw, R. H. J. and Khusnutdinova, K. R. 2006 Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system. Physica D 214, 124.
Guio, P., Borve, S., Daldorff, L. K., Lynov, J. P., Michelsen, P., Pecseli, H. L. and Rasmussen, J. J., Saeki, K. and Trulsen, . 2003 Phase space vortices in collisionless plasmas. J. Nonlinear Process. Geophys. 10, 7586.
Hertzberg, M. P., Cramer, N. F. and Vladimirov, S. V. 2004 Modulational and decay instabilities of Alfven waves in a multicomponent plasma. J. Geophys. Res. 109, A02103(110).
Infeld, E. and Rowlands, G. 1990 Nonlinear Waves, Solitons and Chaos. Cambridge, UK: Cambridge University Press.
Johansson, M. 2006 Discrete nonlinear Schrödinger approximation of a mixed Klein-Gorden/Fermi-Pasta-Ulam chain: modulational instability and a statistical condition for creation of thermodynamic breathers. Physica D 216, 6270.
Jukui, X. 2003 Modulational instability of ion-acoustic waves in a plasma consisting of warm ions and non-thermal electrons. Chaos, Solitons Fractals 18, 849853.
Kakutani, T. and Sugimoto, N. 1974 Krylov-Bogoliuobov-Mitropolsky method for nonlinear wave modulation. Phys. Fluids 17, 16171625.
Kourakis, I., Esfandyari, A., Mehdipoor, M. and Shukla, P. K. 2006 Modulated electrostatic modes in pair plasmas: modulaional stability profile and envelope excitations. Phys. Plasmas 13, 052117(19).
Kourakis, I. and Shukla, P. K. 2004b Modulated wave packets and enveope solitary structures in complex plasmas. IEEE Trans. Plasma Sci. 32, 573581.
Kourakis, I. and Shukla, P. K. 2004a Oblique amplitude modulation of dust-acoustic plasma waves. Phys. Scripta 69, 316327.
Kourakis, I. and Shukla, P. K. 2005c Exact theory for localized envelope modulated electrostatic wavepackets in apace and dusty plasmas. Nonlinear Process. Geophys. 12, 407423.
Kourakis, I., Shukla, P. K., Marklund, M. and Stenflo, L. 2005b Modulational instability criteria for two-component Bose-Einstein condensates. Eur. Phys. J. B 46, 381384.
Kourakis, I., Shukla, P. K. and Morfill, G. 2005a Modulational instability and localized excitations involving two nonlinearly coupled upper-hybrid waves in plasmas. New J. Phys. 7, 153(118).
Kourakis, I., Verheest, F. and Cramer, N. 2007 Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas. Phys. Plasmas 14, 022306.
Law, K. J. H., Kevrekidis, P. G., Frantzeskakis, D. J. and Bishop, A. R. 2008 Emergence of unstable modes in an expanding domain for energy-conserving wave equations. Phys. Lett. A 372, 658664.
McFadden, J. P., Carlson, C. W., Ergun, R. E., Mozer, F. S., Muschietti, L., Roth, I. and Moebius, E. 2003 FAST observations of ion solitary waves. J. Geophys. Res. 108, 8018.
Mishra, M. K. and Chhabra, R. S. 1996 Ion-acoustic compressive and rarefactive solitons in a warm multicomponent plasma with negative ions. Phys. Plasmas 3, 44464454.
Mishra, M. K., Chhabra, R. S. and Sharma, S. R. 1993 Modulational instability of ion-acoustic waves in a plasma with negative ions. Phys. Rev. E 48, 46424647.
Mishra, M. K., Chhabra, R. S. and Sharma, S. R. 1994 Stability of oblique modulation of ion-acoustic waves in a multicomponent plasma. Phys Plasmas 1, 7075.
Mishra, M. K., Chhabra, R. S. and Sharma, S. R. 1995 Nonlinear oblique modulation of ion-acoustic waves in a multicomponent plasma with negative ions Phys. Rev. E 51, 47904795.
Mishra, A. P. and Chowdhury, A. R. 2003 Modulated ion-acoustic wave near criticalness—a new nonlinear Schrödinger equation in a collisional plasma. FIZIKA A 11, 163176.
Mishra, A. P. and Chowdhury, A. R. 2006a Dust-acoustic waves in a self-gravitating complex plasma with trapped electrons and nonisothermal ions. Eur. Phys. J. D 37, 105113.
Mishra, A. P. and Chowdhury, A. R. 2006 Modulational instability of dust acoustic waves in a dusty plasma with nonthermal electrons and ions. Eur. Phys. J. D 39, 4957.
Ndzana, F., Mohamadou, A. and Kofane, T. C. 2007 Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach. Opt. Commun. 275, 421428.
Nohara, B. T., Arimoto, A. and Saigo, T. 2008 Governing equations of envelopes created by nearly bichromatic waves and relation to the nonlinear Schrödinger equation. Chaos Solitons Fractals 35, 942948.
Pottelette, R., Ergun, R. E., Truemann, R. A., Bethomier, M., Carlson, C. W., McFadden, J. P. and Roth, I. 1999 Modulated electron-acoustic waves in auroral density cavities:FAST observations. Geophys. Res. Lett. 26, 26292632.
Rapti, Z., Trombettoni, A., Kevrekidis, P. G., Frantzeskakis, D. J., Malomed, B. A. and Bishop, A. R. 2004 Modulational instabilities and domain walls in coupled discrete nonlinear Schrödinger equations. Phys. Lett. A 330, 95106.
Remoissenet, M. 1994 Waves Called Solitons. Berlin, Germany: Springer-Verlag.
Saeki, K., Michelsen, P., Pecseli, H. L. and Rasmussen, J. J. 1979 Formation and caoalescence of electron solitary holes. Phys. Rev. Lett. 42, 501504.
Sahu, B. and RoyChoudhury, R. 2006 Modulational instability of dust acoustic waves in a dusty plasma with nonthermal electrons and ions. Phys. Plasmas 13, 072302(15).
Salahuddin, M. 2002 Ion-acoustic envelope solitons in electron-positron-ion plasmas. Phys. Rev. E 66, 036407(14).
Shivamogi, B. K. 1988 Introduction to Nonlinear Fluid-Plasma Waves. Doredrecht, The Netherlands: Kluwer Academic Press.
Shukla, P. K., Stenflo, L. and Fedele, R. 2001 Modulational instability of two colliding Bose-Einstein condensates. Phys. Scripta 64, 553.
Singh, S. V. and Lakhina, G. S. 2004 Electron-acoustic solitary waves with nonthermal distribution of electrons. Nonlinear Process Geophys. 11, 275279.
Swider, W. 1988 Ionospheric Modeling (ed. Korenkov, J. N.). Basel, Switzerlsnd: Birkhauser, pp. 403.
Tan, B. and Boyd, J. P. 2001 Stability and long time evolution of the periodic solutions to the two coupled nonlinear Schrödinger equations. Chaos Solitons Fractals 12, 721734.
Tang, R. A. and Jukui, X. 2003 Stability of oblique modulation of dust-acoustic waves in a warm dusty plasma with dust charge variation. Phys. Plasmas 10, 38003803.
Tang, R. A. and Xue, J. K. 2004 Nonthermal electrons and warm ion effects on oblique modulation of ion-acoustic waves. Phys. Plasmas 11, 39393944.
Theocharis, G., Rapti, Z., Kevrekidis, P. G., Frantzeskakis, D. J. and Konotop, V. V. 2003 Modulational instability of Gross-Pitaevskii-type equations in 1+1 dimensions. Phys. Rev. A 67, 063610(18).
Tstovich, V. and Wharton, C. B. 1978 Laboratory electron-positron plasma. A new research object. Comments Plasma Phys. Control. Fusion 4, 91100.
Tsukabayashi, I. and Nakamura, Y. 1990 Abstract no. 139200. Phys. Absr. 93, 1388.
Verheest, F., Hellberg, M. A., Gray, G. J. and Mace, R. L. 1995 Electrostatic solitons in multispecies electron-positron plasmas. Astrophys. Space Sci. 239, 125139.
Vladimirov, S. V., Tsytovich, V. N., Popel, S. I. and Khakimov, F. K. 1995 Modulational Interactions in Plasmas. Norwell, MA.: Kluwer Academic Press.
Washimi, H. and Taniuti, T. 1966 Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996998.
Watanabe, W. 1977 Self-modulation of a nonlinear ion wave packet. J. Plasma Phys. 17, 487501.
Whitam, G. B. 1967 Nonlinear-dispersion of water waves. J. Fluid Mech. 27, 399412.
Xue, J. 2004a Modulational instability of multi-dimensional dust ion-acoustic waves. Phys. Lett. A 330, 390395.
Xue, J. 2004 Propagation of nonplanar dust-acoustic envelope solitary waves in a two-ion-temperature dusy plasma. Phys. Plasmas 11, 18601865.
Xue, J. 2005 Modulational instability of the trapped Bose-Einstein condensates. Phys. Lett. A 341, 527531.
Xue, J. and He, L. 2003 Modulational instability of cylindrical and spherical dust ion-acoustic waves. Phys. Plasmas 10, 339342.
Yemele, D. and Marquie, P. 2003 Chaotic-like behaviour of modulated waves in a nonlinear discrete LC transmission line. Chaos Solitons Fractals 15, 465473.
Zhu, S. 2007 Exact solutions for the high order dispersive cubic-quintic nonlinear Schrödinger equation by extended hyperbolic auxiliary equation method. Chaos Solitons Fractals 34, 16081612.
MathJax is a JavaScript display engine for mathematics. For more information see


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed