Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-26T06:40:02.225Z Has data issue: false hasContentIssue false
  • English
  • Français

An analytical study on the existence of solitary structure at M = Mc

Published online by Cambridge University Press:  17 April 2012

ANIMESH DAS ,
ANUP BANDYOPADHYAY  and
K. P. DAS
ANIMESH DAS
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700 032, India ([email protected])
ANUP BANDYOPADHYAY
Affiliation:
Department of Mathematics, Jadavpur University, Kolkata 700 032, India ([email protected])
K. P. DAS
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009, India
Get access Rights & Permissions [Opens in a new window]

Abstract

A general theory for the existence of solitary structure at M = Mc has been discussed, where Mc is the lower bound of the Mach number M, i.e., solitary structures start to exist for M > Mc. Three important results have been proved to confirm the existence of solitary structure at M = Mc. If V(φ)(≡ V(M,φ)) denotes the Sagdeev potential with φ being the perturbed field or perturbed dependent variable associated with a specific problem, V(M, φ) is well defined as a real number for all M ∈ ℳ and φ ∈ Φ0, and V(M, 0) = V′(M, 0) = V″(Mc, 0) = 0, V‴(Mc, 0) < 0 (V‴(Mc, 0) > 0), ∂ V/∂ M < 0 for all M (∈ ℳ) > 0 and φ (∈ Φ0) > 0 (φ (∈ Φ0) < 0), where ‘′ ≡ ∂/∂φ’, the main analytical results for the existence of solitary wave or double layer solution of the energy integral at M = Mc are as follows. Result 1: If there exists at least one value M0 of M such that the system supports positive (negative) potential solitary waves for all Mc < M < M0, then there exists either a positive (negative) potential solitary wave or a positive (negative) potential double layer at M = Mc. Result 2: If the system supports only negative (positive) potential solitary waves for M > Mc, then there does not exist positive (negative) potential solitary wave at M = Mc. Result 3: It is not possible to have coexistence of both positive and negative potential solitary structures at M = Mc. Apart from the conditions of Result 1, the double layer solution at M = Mc is possible only when there exists a double layer solution in any right neighborhood of Mc. Finally, these analytical results have been applied to a specific problem on dust acoustic (DA) waves in non-thermal plasma in search of new results.

Type
Papers
Information
Journal of Plasma Physics , Volume 78 , Issue 5 , October 2012 , pp. 565 - 584
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baboolal, S., Bharuthram, R. and Hellberg, M. A. 1988 Arbitrary-amplitude rarefactive ion-acoustic double layers in warm multi-fluid plasmas. J. Plasma. Phys. 40, 163–178.CrossRefGoogle Scholar
Baboolal, S., Bharuthram, R. and Hellberg, M. A. 1989 Arbitrary-amplitude theory of ion-acoustic solitons in warm multi-fluid plasmas. J. Plasma. Phys. 41, 341–353.CrossRefGoogle Scholar
Baboolal, S., Bharuthram, R. and Hellberg, M. A. 1990 Cut-off conditions and existence domains for large-amplitude ion-acoustic solitons and double layers in fluid plasmas. J. Plasma. Phys. 44, 1–23.CrossRefGoogle Scholar
Baboolal, S., Bharuthram, R. and Hellberg, M. A. 1991 On the existence of ion-acoustic double layers in negative-ion plasmas. J. Plasma. Phys. 46, 247–254.CrossRefGoogle Scholar
Baluku, T. K. and Hellberg, M. A. 2008 Dust acoustic solitons in plasmas with kappa-distributed electrons and/or ions. Phys. Plasmas 15, 123705-1–123705-11.CrossRefGoogle Scholar
Baluku, T. K., Hellberg, M. A., Kourakis, I. and Saini, N. S. 2010a Dust ion acoustic solitons in a plasma with kappa-distributed electrons. Phys. Plasmas 17, 053702-1–053702-11.CrossRefGoogle Scholar
Baluku, T. K., Hellberg, M. A. and Verheest, F. 2010b New light on ion acoustic solitary waves in a plasma with two-temperature electrons. EPL 91, 15001-p1–15001-p6.CrossRefGoogle Scholar
Bharuthram, R. and Shukla, P. K. 1986 Large amplitude ion-acoustic double layers in a double Maxwellian electron plasma. Phys. Fluids. 29, 3214–3218.CrossRefGoogle Scholar
Cairns, R. A., Bingham, R., Dendy, R. O., Nairn, C. M. C., Shukla, P. K. and Mamun, A. A. 1995a Ion sound solitary waves with density depressions. J. Phys. IV 5, C6-43–C6-48.Google Scholar
Cairns, R. A., Mamun, A. A., Bingham, R., Böstrom, R., Dendy, R. O., Nairn, C. M. C. and Shukla, P. K. 1995b Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709–2712.CrossRefGoogle Scholar
Cairns, R. A., Mamun, A. A., Bingham, R. and Shukla, P. K. 1996 Ion-acoustic solitons in a magnetized plasma with nonthermal electrons. Phys. Scripta T63, 80–86.CrossRefGoogle Scholar
Das, A., Bandyopadhyay, A. and Das, K. P. 2009 Arbitrary amplitude dust acoustic solitary waves and double layers in nonthermal plasma, including the effect of dust temperature. Phys. Plasmas 16, 073703-1–073703-10.CrossRefGoogle Scholar
Das, A., Bandyopadhyay, A. and Das, K. P. 2010 Large amplitude dust acoustic solitary waves and double layers in positively charged warm dusty plasma with nonthermal electrons. Phys. Plasmas 17, 014503-1–014503-4.CrossRefGoogle Scholar
Das, A., Bandyopadhyay, A. and Das, K. P. 2012 Dust ion-acoustic solitary structures in non-thermal dusty plasma. J. Plasma. Phys. 78, 149–164.CrossRefGoogle Scholar
Djebli, M. and Marif, H. 2009 Large amplitude double layers in a positively charged dusty plasma with nonthermal electrons. Phys. Plasmas 16, 063708-1–063708-8.CrossRefGoogle Scholar
Dubinov, A. E. 2009 On a widespread inaccuracy in defining the Mach number of solitons in a plasma. Plasma Phys. Rep. 35, 991–992.CrossRefGoogle Scholar
Gill, T. S., Kaur, H. and Saini, N. S. 2003 Ion-acoustic solitons in a plasma consisting of positive and negative ions with nonisothermal electrons. Phys. Plasmas 10, 3927–3932.CrossRefGoogle Scholar
Hellberg, M. A., Verheest, F. and Cattaert, T. 2006 Existence domains for nonlinear structures in complex two-ion-temperature plasmas. J. Phys. A: Math. Gen. 39, 3137–3146.CrossRefGoogle Scholar
Maharaj, S. K., Pillay, S. R., Bharuthram, R., Reddy, R. V., Singh, S. V. and Lakhina, G. S. 2006 Arbitrary amplitude dust-acoustic double layers in a non-thermal plasma. J. Plasma Phys. 72, 43–58.CrossRefGoogle Scholar
Maharaj, S. K., Pillay, S. R., Bharuthram, R., Singh, S. V. and Lakhina, G. S. 2004 The effect of dust grain temperature and dust streaming on electrostatic solitary structures in a non-thermal plasma. Phys. Scripta T113, 135–140.CrossRefGoogle Scholar
Mamun, A. A., Cairns, R. A., and Shukla, P. K. 1996a Solitary potentials in dusty plasmas. Phys. Plasmas 3, 702–704.CrossRefGoogle Scholar
Mamun, A. A., Cairns, R. A., and Shukla, P. K. 1996b Effects of vortex-like and non-thermal ion distributions on non-linear dust-acoustic waves. Phys. Plasmas 3, 2610–2614.CrossRefGoogle Scholar
Mendoza-Briceño, C. A., Russel, S. M. and Mamun, A. A. 2000 Large amplitude electrostatic solitary structures in a hot non-thermal dusty plasma. Planet. Space Sci. 48, 599–608.CrossRefGoogle Scholar
Popel, S. I., Yu, M. Y. and Tsytovich, V. N. 1996 Shock waves in plasmas containing variable-charge impurities. Phys. Plasmas 3, 4313–4315.CrossRefGoogle Scholar
Sagdeev, R. Z. 1966 Reviews of Plasma Physics, vol. 4 (ed. Leontovich, M. A.). New York: Consultant Bureau.Google Scholar
Shukla, P. K. and Yu, M. Y. 1978 Exact solitary ion acoustic waves in a magnetoplasma. J. Math. Phys. 19, 2506–2508.CrossRefGoogle Scholar
Tanjia, F. and Mamun, A. A. 2008 Arbitrary amplitude electro-acoustic solitary waves in an adiabatic dusty plasma. Phys. Scr. 78, 065502-1–065502-6.CrossRefGoogle Scholar
Verheest, F. 2000 Waves in Dusty Space Plasmas. New York: Kluwer, pp. 105–108.CrossRefGoogle Scholar
Verheest, F. 2009 Nonlinear acoustic waves in nonthermal plasmas with negative and positive dust. Phys. Plasmas 16, 013704-1–013704-9.CrossRefGoogle Scholar
Verheest, F. 2010 Nonlinear acoustic waves in nonthermal dusty or pair plasmas. Phys. Plasmas 17, 062302-1–062302-10.CrossRefGoogle Scholar
Verheest, F. and Hellberg, M. A. 2010 Nonthermal effects on existence domains for dust-acoustic solitary structures in plasmas with two-temperature ions. Phys. Plasmas 17, 023701-1–023701-10.CrossRefGoogle Scholar
Verheest, F. and Pillay, S. R. 2008 Large amplitude dust-acoustic solitary waves and double layers in nonthermal plasmas. Phys. Plasmas 15, 013703-1–013703-11.CrossRefGoogle Scholar
Xie, B., He, K. and Huang, Z. 1998 Effect of adiabatic variation of dust charges on dust-acoustic solitary waves. Phys. Lett. A 247, 403–409.CrossRefGoogle Scholar
Yu, M. Y., Shukla, P. K. and Bujarbarua, S. 1980 Fully nonlinear ion-acoustic solitary waves in a magnetized plasma. Phys. Fluids 23, 2146–2147.CrossRefGoogle Scholar