Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

doi:10.1088/1674-1056/23/7/070505

›› 2014, Vol. 23 ›› Issue (7): 70505-070505.doi: 10.1088/1674-1056/23/7/070505

Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

Emad K. El-Shewy, Abeer A. Mahmoud, Ashraf M. Tawfik, Essam M. Abulwafa, Ahmed Elgarayhi

Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt

收稿日期:2013-09-11 修回日期:2014-01-02 出版日期:2014-07-15 发布日期:2014-07-15

Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

Emad K. El-Shewy, Abeer A. Mahmoud, Ashraf M. Tawfik, Essam M. Abulwafa, Ahmed Elgarayhi

Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt

Received:2013-09-11 Revised:2014-01-02 Online:2014-07-15 Published:2014-07-15
Contact: Essam M. Abulwafa E-mail:abulwafa@mans.edu.eg
About author:05.45.Df; 52.30.-q; 52.27.Lw; 52.35.Fp

摘要/Abstract

摘要： The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non-thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

关键词: dust-acoustic waves, reductive perturbation method, modified Riemann-Liouville fractional derivative, space-time fractional KdV-Burgers equation

Abstract: The KdV-Burgers equation for dust acoustic waves in unmagnetized plasma having electrons, singly charged non-thermal ions, and hot and cold dust species is derived using the reductive perturbation method. The Boltzmann distribution is used for electrons in the presence of the cold (hot) dust viscosity coefficients. The semi-inverse method and Agrawal variational technique are applied to formulate the space-time fractional KdV-Burgers equation which is solved using the fractional sub-equation method. The effect of the fractional parameter on the behavior of the dust acoustic shock waves in the dusty plasma is investigated.

Key words: dust-acoustic waves, reductive perturbation method, modified Riemann-Liouville fractional derivative, space-time fractional KdV-Burgers equation

中图分类号: (Fractals)

05.45.Df

52.30.-q (Plasma dynamics and flow) 52.27.Lw (Dusty or complex plasmas; plasma crystals) 52.35.Fp (Electrostatic waves and oscillations (e.g., ion-acoustic waves))

Emad K. El-Shewy, Abeer A. Mahmoud, Ashraf M. Tawfik, Essam M. Abulwafa, Ahmed Elgarayhi. Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions[J]. , 2014, 23(7): 70505-070505.

参考文献 51

[1]	Shukla P K and Mamun A A 2002 Introduction to Dusty Plasma Physics (Bristol: Institute of Physics)
[2]	Zhang L P and Xue J K 2008 Chin. Phys. B 17 2594
[3]	Guo Z R, Yang Z Q, Yin B X and Sun M Z 2010 Chin. Phys. B 19 115203
[4]	Qi X H, Duan W S, Chen J M and Wang S J 2011 Chin. Phys. B 20 025203
[5]	Yang X F, Wang S J, Chen J M, Shi Y R, Lin M M and Duan W S 2012 Chin. Phys. B 21 055202
[6]	Ren Y C, Wang X S and Wang X G 2012 Chin. Phys B 21 115201
[7]	Akhtar N, Mahmood S and Saleem H 2007 Phys. Lett. A 361 126
[8]	Asbridge J R, Bame S J and Strong I B 1968 J. Geophys. Res. 73 5777
[9]	Feldman W C, Anderson S J, Bame S J, Gary S P, Gosling J T, McComas D J, Thomsen M F, Paschmann G and Hoppe M M 1983 J. Geophys. Res. 88 96
[10]	Elwakil S A, Elgarayhi A, El-Shewy E K, Mahmoud A A and El-Attafi M A 2013 Astrophys. Space Sci. 343 661
[11]	Nakamura Y and Sarma A 2001 Phys. Plasmas 8 3921
[12]	Duha S S, Anowar M G M and Mamun A A 2010 Phys. Plasmas 17 03711
[13]	Nakamura Y, Bailung H and Shukla P K 1999 Phys. Rev. Lett. 83 1602
[14]	Mamun A A and Tasnim S 2010 Phys. Plasmas 17 073704
[15]	Misra A P 2009 Phys. Plasmas 16 033702
[16]	El-Shewy E K, Abdelwahed H G and Elmessary M A 2011 Phys. Plasmas 18 113702
[17]	Xu H Y, Qi H T and Jiang X Y 2013 Chin. Phys. B 22 014401
[18]	Liu J G 2013 Chin. Phys. B 22 060510
[19]	Kumar R and Gupta V 2013 Chin. Phys. B 22 074601
[20]	Dong X J, Hu Y F, Wu Y Y, Zhao J and Wan Z Z 2010 Chin. Phys. Lett. 27 044401
[21]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[22]	Kilbas A A, Srivastava H M and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier)
[23]	Jumarie G 2009 Appl. Math. Lett. 22 378
[24]	Jumarie G 2010 Nonlinear Anal. Real World Appl. 11 535
[25]	Abulwafa E M, Elgarayhi A M, Mahmoud A A and Tawfik A M 2013 Comput. Meth. Sci. Tech. 19 235
[26]	Ghany H A, Okb El Bab A S, Zabel A M and Hyder A A 2013 Chin. Phys. B 22 080501
[27]	Jiang X and Qi H 2012 J. Phys. A: Math. Theor. 45 485101
[28]	Riewe F 1996 Phys. Rev. E 53 1890
[29]	Riewe F 1997 Phys. Rev. E 55 3581
[30]	Agrawal O P 2002 J. Math. Anal. Appl. 272 368
[31]	Agrawal O P 2008 J. Math. Anal. Appl. 337 1
[32]	Zhou S, Fu J L and Liu Y S 2010 Chin. Phys. B 19 120301
[33]	Zhang Y 2012 Chin. Phys. B 21 084502
[34]	Zhang S H, Chen B Y and Fu J L 2012 Chin. Phys. B 21 100202
[35]	Wei H Y and Xia T C 2012 Chin. Phys. B 21 110203
[36]	El-Wakil S A, Abulwafa E M, El-Shewy E K and Mahmoud A A 2011 Chin. Phys. B 20 040508
[37]	El-Wakil S A, Abulwafa E M, El-Shewy E K and Mahmoud A A 2012 Adv. Space Res. 49 1721
[38]	El-Wakil S A, Abulwafa E M, El-Shewy E K and Mahmoud A A 2013 Astrophys Space Sci. 346 383
[39]	Zhang S, Zong Q A, Liu D and Gao Q 2010 Commun. Fract. Calcul. 1 48
[40]	Zhang S and Zhang H Q 2011 Phys. Lett. A 375 1069
[41]	Guo S, Mei L, Li Y and Sun Y 2012 Phys. Lett. A 376 407
[42]	Ge H X, Liu Y Q and Cheng R J 2012 Chin. Phys. B 21 10206
[43]	Wu G C 2012 Chin. Phys. B 21 120504
[44]	Gepreel K A and Mohamed M S 2013 Chin. Phys. B 22 010201
[45]	He J H 1997 Int. J. Turbo Jet-Eng. 14 23
[46]	He J H 2004 Chaos Soliton. Fract. 19 847
[47]	He J H and Lee E W M 2009 Phys. Lett. A 373 1644
[48]	Cao X Q, Song J Q, Zhang W M and Zhao J 2011 Chin. Phys. B 20 090401
[49]	Yao L, Yang Y J and Zhou X W 2013 Abstr. Appl. Anal. 2013 931643
[50]	Washimi H and Taniuti T 1966 Phys. Rev. Lett. 17 996
[51]	He J H 2006 Int. J. Mod. Phys. B 20 1141

Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

Space–time fractional KdV–Burgers equation for dust acoustic shock waves in dusty plasma with non-thermal ions

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