Abstract
The properties of cylindrical and spherical dust acoustic (DA) solitary and shock waves in an unmagnetized electron depleted dusty plasma consisting of inertial dust fluid and ions featuring Tsallis statistics are investigated by employing the reductive perturbation technique. A Korteweg-de Vries Burgers (KdVB) equation is derived and its numerical solution is obtained. The effects of ion nonextensivity and dust kinematic viscosity on the basic features of DA solitary and shock waves are discussed in nonplanar geometry. It is found that nonextensive nonplanar DA waves behave quite differently from their one-dimensional planar counterpart.
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Abdelsalam, U.M., Moslem, W.M., Khater, A.H., Shukla, P.K.: Phys. Plasmas 18, 092305 (2011)
Ablowitz, M.J., Clarkson, P.A.: Solitons, Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge (1991)
Ait Gougam, L., Tribeche, M.: Astrophys. Space Sci. 331, 181 (2011)
Alinejad, H.: Astrophys. Space Sci. 327, 131 (2010)
Amour, R., Tribeche, M.: Phys. Plasmas 17, 063702 (2010)
Bacha, M., Tribeche, M.: Astrophys. Space Sci. (2011). doi:10.1007/s10509-011-0830-7
Bains, A.S., Tribeche, M., Gill, T.S.: Phys. Lett. A 375, 2059 (2011)
Barkan, A., Merlino, R.L., D’Angelo, N.: Phys. Plasmas 2, 3563 (1995)
Du, J.: Phys. Lett. A 329, 262 (2004)
El-Awady, E.I., Moslem, W.M.: Phys. Plasmas 18, 082306 (2011)
Eslami, P., Mottaghizadeh, M., Pakzad, H.R.: Phys. Scr. 83, 065502 (2011)
Goertz, C.K.: Rev. Geophys. 27, 271 (1989)
Haq, M.N.-ul., Saeed, R., Shah, A.: J. Appl. Phys. 108, 043301 (2010)
Havnes, O.: In: Bharuthram, R., Hellberg, M.A., Shukla, P.K., Verheest, F. (eds.) Dusty Plasmas in the New Millennium. AIP, Melville (2002)
Hirota, R.: Phys. Rev. Lett. 27, 1192 (1971)
Khan, S.A., Mahmood, S., Mirza, A.M.: Phys. Lett. A 372, 148 (2008)
Liu, B., Goree, J.: Phys. Rev. Lett. 100, 055003 (2008)
Liu, Z., Du, J.: Phys. Plasmas 16, 123707 (2009)
Liu, Z., Liu, L., Du, J.: Phys. Plasmas 16, 072111 (2009)
Liu, H.F., Wang, S.Q., Li, C.Z., Xiang, Q., Yang, F.Z., Liu, Y.: Phys. Scr. 82, 065402 (2010)
Liyan, L., Du, J.: Physica A 387, 4821 (2008)
Mamun, A.A., Shukla, P.K.: Phys. Lett. A 290, 173 (2001)
Mamun, A.A., Shukla, P.K.: Phys. Plasmas 9, 1468 (2002)
Mamun, A.A., Shukla, P.K.: Phys. Rev. E 80, 037401 (2009)
Mamun, A.A., Shukla, P.K.: Phys. Lett. A 374, 472 (2010)
Mamun, A.A., Cairns, R.A., Shukla, P.K.: Phys. Plasmas 3, 702 (1996)
Mendis, D.A., Rosenberg, M.: Annu. Rev. Astron. Astrophys. 32, 419 (1994)
Miura, M.R.: Backlund Transformation. Springer, Berlin (1978)
Moghanjoughi, A.: Astrophys. Space Sci. (2011). doi:10.1007/s10509-011-0876-6
Pakzad, H.R.: Astrophys. Space Sci. 330, 301 (2010)
Pakzad, H.R., Tribeche, M.: Astrophys. Space Sci. 334, 45 (2011)
Rao, N.N., Shukla, P.K., Yu, M.Y.: Planet. Space Sci. 38, 543 (1990)
Roychoudhury, R., Das, G.C., Sarma, J.: Phys. Plasmas 6, 2721 (1999)
Sabry, R., Moslem, W.M., Shukla, P.K., Saleem, H.: Phys. Rev. E 79, 056402 (2009)
Sahu, B.: Phys. Scr. 82, 065504 (2010)
Shukla, P.K.: Phys. Plasmas 8, 1447 (2001)
Shukla, P.K., Mamun, A.A.: Introduction to Dusty Plasma Physics. Institute of Physics, Bristol (2002)
Shukla, P.K., Silin, V.P.: Phys. Scr. 45, 508 (1992)
Silva, R., Plastino, A.R., Lima, J.A.S.: Phys. Lett. A 249, 401 (1998)
Tribeche, M., Merriche, A.: Phys. Plasmas 18, 034502 (2011)
Tribeche, M., Houili, H., Zerguini, T.H.: Phys. Plasmas 9, 419 (2002)
Tribeche, M., Djebarni, L., Amour, R.: Phys. Plasmas 17, 042114 (2010)
Tsallis, C.: J. Stat. Phys. 52, 479 (1988)
Verheest, F.: Space Sci. Rev. 77, 267 (1996)
Verheest, F.: Waves in Dusty Space Plasmas. Kluwer, Dordrecht (2000)
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Sahu, B., Tribeche, M. Nonextensive dust acoustic solitary and shock waves in nonplanar geometry. Astrophys Space Sci 338, 259–264 (2012). https://doi.org/10.1007/s10509-011-0941-1
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DOI: https://doi.org/10.1007/s10509-011-0941-1