Ion acoustic solitons of KdV and modified KdV equations in weakly relativistic plasma containing nonthermal electron, positron and warm ion. (English) Zbl 1237.85026
Summary: The ion-acoustic solitons in a weakly relativistic electron-positron-ion plasma have been investigated. Relativistic ions, Maxwell-Boltzmann distributed positrons and nonthermal electrons are considered in collisionless warm plasma. Using a reductive perturbation theory, a Korteweg-de Vries (KdV) equation is derived, and the relativistic effect on the solitons is studied. It is found that the amplitude of solitary waves of the KdV equation diverges at the critical values of plasma parameters. Finally, in this situation, the solitons of a modified KdV (mKdV) equation with finite amplitude is derived.
MSC:
| 85A25 | Radiative transfer in astronomy and astrophysics |
| 35Q51 | Soliton equations |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 83C10 | Equations of motion in general relativity and gravitational theory |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
References:
| [1] | Arons, J.: Space Sci. Rev. 24, 417 (1979) · doi:10.1007/BF00172212 |
| [2] | Bandyopadhyay, A., Das, K.P.: Phys. Scr. 63, 145 (2001) · Zbl 1115.76428 · doi:10.1238/Physica.Regular.063a00145 |
| [3] | Bharuthram, R., Shukla, P.K.: Phys. Fluids 20, 3214 (1986) · Zbl 0602.76117 · doi:10.1063/1.865839 |
| [4] | Carins, RA, Bingham, R., Dendy, R.O., Nairn, C.M.C., Shukla, P.K., Mamun, A.A.: J. Phys. (France) IV 5C6, 43 (1995b) |
| [5] | Carins, RA, Mamun, A.A., Bingham, R., Bostrom, R., Dendy, R.O., Nairn, C.M.C. et al.: Geophys. Res. Lett. 22, 2709 (1995a) · doi:10.1029/95GL02781 |
| [6] | Carins, RA, Mamun, A.A., Bingham, R., Shukla, P.K.: Phys. Scr. T63, 80 (1996) · doi:10.1088/0031-8949/1996/T63/012 |
| [7] | Das, G.C., Paul, S.N.: Phys. Fluids 28, 823 (1985) · Zbl 0586.76208 · doi:10.1063/1.865050 |
| [8] | Dovner, P.O., Eriksson, AI, Bostrom, R., Holback, B.: Geophys. Res. Lett. 21, 1827 (1994) · doi:10.1029/94GL00886 |
| [9] | El-Labany, S.K., El-Taibany, W.F.: Phys. Plasmas 10, 989 (2003) · doi:10.1063/1.1557912 |
| [10] | EL-Labany, S.K., Shaaban, S.M.: J. Plasma Phys. 53, 245 (1995) · doi:10.1017/S0022377800018158 |
| [11] | EL-Labany, S.K., Nafie, H.O., EL-Sheikh, A.: J. Plasma Phys. 56, 13 (1996) · doi:10.1017/S002237780001905X |
| [12] | Gill, T.S., Singh, A., Kaur, H., Saini, N.S., Bala, P.: Phys. Lett. A 361, 346 (2007) · doi:10.1016/j.physleta.2006.09.053 |
| [13] | Goldreich, P., Julian, W.H.: Astrophys. J. 157, 869 (1969) · doi:10.1086/150119 |
| [14] | Grabbe, C.: J. Geophys. Res. 94, 17299 (1989) · doi:10.1029/JA094iA12p17299 |
| [15] | Hall, D.S., Chaloner, C.P., Bryant, D.A., Lepine, D.R., Trikakis, J.: Geophys. Res. 96, 7869 (1991) · doi:10.1029/90JA02137 |
| [16] | Ikezi, H.: Phys. Fluids 16, 1668 (1973) · doi:10.1063/1.1694194 |
| [17] | Kalita, B.C., Barman, S.N., Goswami, G.: Phys. Plasmas 3, 145 (1996) · doi:10.1063/1.871840 |
| [18] | Kaur, H., Gill, T.S., Saini, N.S.: Chaos Solitons Fractals 42, 1638 (2009) · Zbl 1198.82010 · doi:10.1016/j.chaos.2009.03.065 |
| [19] | Kuehl, H.H., Zhang, G.Y.: Phys. Fluids B 3, 26 (1991) · doi:10.1063/1.859946 |
| [20] | Lundin, R., Eliasson, L., Hultquist, B., Stastewicz, K.: Geophys. Res. Lett. 14, 443 (1987) · doi:10.1029/GL014i004p00443 |
| [21] | Mahmood, S., Saleem, H.: Phys. Plasmas 9, 724 (2002) · doi:10.1063/1.1433663 |
| [22] | Mamun, A.A.: Eur. Phys. J. D 11, 143 (2000) |
| [23] | Masood, W., Jehan, N., Mirza, A.M., Sakanaka, P.H.: Phys. Lett. A 372, 4279 (2008) · Zbl 1221.76110 · doi:10.1016/j.physleta.2008.03.058 |
| [24] | Michel, F.C.: Rev. Mod. Phys. 54, 1 (1982) · doi:10.1103/RevModPhys.54.1 |
| [25] | Miller, H.R., Witta, P.J.: Active Galactic Nuclei, p. 202. Springer, Berlin (1987), |
| [26] | Misner, W., Thorne, K.S., Wheeler, J.I.: Gravitation, p. 763. Freeman, San Francisco (1973), |
| [27] | Misra, A.P., Bhowmik, C.: Phys. Lett. A 369, 90 (2007) · doi:10.1016/j.physleta.2007.04.066 |
| [28] | Mushtaq, A., Shah, H.A.: Phys. Plasmas 12, 012301 (2005) |
| [29] | Nejoh, Y.: J. Plasma Phys. 37, 487 (1987) · doi:10.1017/S0022377800012320 |
| [30] | Nejoh, Y.: J. Plasma Phys. 38, 439 (1987) · doi:10.1017/S0022377800012708 |
| [31] | Nejoh, Y.N.: Aust. J. Phys. 50, 309 (1997) · doi:10.1071/P96064 |
| [32] | Rees, M.J.: In: The Very Early Universe, Gibbson, G.W., Hawking, S.W., Siklas, S. (eds.) Cambridge University Press, Cambridge (1983) |
| [33] | Rizzato, F.B.: J. Plasma Phys. 40, 289 (1988) · doi:10.1017/S0022377800013283 |
| [34] | Shukla, P.K.: Phys. Plasmas 10, 1619 (2003) · doi:10.1063/1.1557071 |
| [35] | Singh, S., Honzawa, T.: Phys. Fluids B 5, 2093 (1993) · doi:10.1063/1.860745 |
| [36] | Surko, C.M., Murphy, T.: Phys. Fluids B 2, 1372 (1990) · doi:10.1063/1.859558 |
| [37] | Surko, C.M., et al.: Rev. Sci. Instrum. 57, 1862 (1986) · doi:10.1063/1.1139154 |
| [38] | Tagare, S.G.: Plasma Phys. 15, 1247 (1973) · doi:10.1088/0032-1028/15/12/007 |
| [39] | Tian, B., Gao, Y.T.: Phys. Lett. A 362, 283 (2007) · Zbl 1197.82028 · doi:10.1016/j.physleta.2006.10.094 |
| [40] | Verheest, F.: Space Sci. Rev. 77, 267 (1996) · doi:10.1007/BF00226225 |
| [41] | Vette, J.I.: Summary of particle population in the magnetosphere. In: Particle and Fields in the Magnetosphere, p. 305. Reidel, Dordrecht (1970) |
| [42] | Washimi, H., Taniuti, T.: Phys. Rev. Lett. 17, 996 (1996) · doi:10.1103/PhysRevLett.17.996 |
| [43] | Yadav, L.L., Sharma, S.R.: Phys. Scr. 43, 106 (1991) · doi:10.1088/0031-8949/43/1/018 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
