| PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES |
|
|
|
|
On Time-Fractional Cylindrical Nonlinear Equation |
| H. G. Abdelwahed1**, E. K. ElShewy2, A. A. Mahmoud2 |
1College of Science and Humanitarian Studies, Physics Department, Prince Sattam Bin Abdul Aziz University, Kingdom of Saudi Arabia
2Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
|
|
| Cite this article: |
|
H. G. Abdelwahed, E. K. ElShewy, A. A. Mahmoud 2016 Chin. Phys. Lett. 33 115201 |
|
|
|
|
Abstract Properties of cylindrical electron acoustic solitons are studied in vortex plasmas. The modified cylindrical Korteweg–de Vries (KdV) equation is acquired and converted into the time fractional cylindrical modified KdV equation by Agrawal's analysis. Via the Adomian decomposition method, a cylindrical soliton solution to the equation is obtained. The cylindrical time fractional effect on the wave properties is investigated. Further, the increase of the fractional order of time $\alpha$ and hot to trapped electrons temperature $\beta$ are minimized in both solitary width and amplitude. These influences on the structures of the soliton may be an alternative to the use of higher order perturbation analysis.
|
|
|
Received: 16 June 2016
Published: 28 November 2016
|
|
| PACS: |
52.30.-q
|
(Plasma dynamics and flow)
|
| |
05.45.Df
|
(Fractals)
|
| |
52.35.Fp
|
(Electrostatic waves and oscillations (e.g., ion-acoustic waves))
|
| |
52.27.Lw
|
(Dusty or complex plasmas; plasma crystals)
|
|
|
| Fund: Supported by the Deanship of Scientific Research at Prince Sattam Bin Abdulaziz University under Grant No 2016/01/6239. |
|
|
|
| [1] | Dubouloz N, Pottelette R, Malingre M and Treumann R A 1991 Geophys. Res. Lett. 18 155 | | [2] | Singh S V and Lakhina G S 2001 Planet. Space Sci. 49 107 | | [3] | Elwakil S A, Zahran M A and El-Shewy E K 2007 Phys. Scr. 75 803 | | [4] | Demiray H 2016 Phys. Plasmas 23 032109 | | [5] | Devanandhan S, Singh S V, Lakhina G S and Bharuthram R 2012 Phys. Plasmas 19 082314 | | [6] | Williams G, Verheest F, Hellberg M A, Anowar M G M and Kourakis I 2014 Phys. Plasmas 21 092103 | | [7] | Abdelwahed H G 2015 Phys. Plasmas 22 092102 | | [8] | Bernstein I B, Greene J M and Kruskal M D 1957 Phys. Rev. 108 546 | | [9] | Lu Q M, Wang D Y and Wang S 2005 J. Geophys. Res. 110 A03223 | | [10] | Lu Q M, Lembege B, Tao J B and Wang S 2008 J. Geophys. Res. 113 A11219 | | [11] | Wu M Y, Wu H, Lu Q M and Xue B S 2010 Chin. Phys. Lett. 27 095201 | | [12] | El-Taibany W F and Moslem W M 2005 Phys. Plasmas 12 032307 | | [13] | Lu, Q M, Wang S and Xiankang D 2005 Phys. Plasmas 12 072903 | | [14] | Sabry R and Omran M A 2013 Astrophys. Space Sci. 344 455 | | [15] | Moslem W M, Abdelsalam U M, Sabry R, El-Shamy E F and El-Labany S K 2010 J. Plasma Phys. 76 453 | | [16] | Mamun A A and Shukla P K 2009 Phys. Rev. E 80 037401 | | [17] | Borhanian J and Shahmansouri M 2013 Phys. Plasmas 20 013707 | | [18] | Mannan A and Mamun A A 2012 Astrophys. Space Sci. 340 109 | | [19] | Pakzad H R 2011 Phys. Plasmas 18 082105 | | [20] | Shuchy S T, Mannan A and Mamun A A 2012 JETP Lett. 95 282 | | [21] | Borhanian J and Shahmansouri M 2012 Astrophys. Space Sci. 342 401 | | [22] | Schamel H 1973 J. Plasma Phys. 9 377 | | [23] | Mamun A A and Shukla P K 2002 J. Geophys. Res. 107 1135 | | [24] | Elwakil S A, El-Shewy E K and Zahran, M A 2004 Chaos Solitons Fractals 22 13 | | [25] | Sahu B and Roychoudhury R 2004 J. Plasma Phys. 11 1947 | | [26] | Frederico G S F and Torres D F M 2008 Nonlinear Dyn. 53 215 | | [27] | Agrawal O P 2008 J. Math. Anal. Appl. 337 1 | | [28] | Wang G W and Xu T Z 2014 Nonlinear Dyn. 76 571 | | [29] | El-Wakil S A, Abulwafa E M, El-Shewy E K and Mahmoud A A 2012 Plasma Phys. 78 641 | | [30] | El-Wakil S A, Abulwafa E M, El-Shewy E K and Mahmoud A A 2012 Adv. Space Res. 49 1721 | | [31] | El-Shewy E K, Mahmoud A A, Tawfik A M, Abulwafa E M and Elgarayhi A 2014 Chin. Phys. B 23 070505 | | [32] | El-Wakil S A, Abulwafa E M, El-Shewy E K and Mahmoud A A 2011 Chin. Phys. B 20 040508 | | [33] | Nazari-Golshan A, Nourazar S S, Parvin P and Ghafoori-Fard H 2014 Astrophys. Space Sci. 349 205 | | [34] | Guo, L M and Zhang Z 2015 Phys. Plasmas 22 052306 | | [35] | Demiray H and Bay?nd?r C 2015 Phys. Plasmas 22 092105 | | [36] | Agrawal O P 2007 J. Phys. A 40 6287 | | [37] | Momian S and Odibat Z 2007 Chaos Solitons Fractals 31 5 1248 | | [38] | Ray S S and Bera R K 2005 Appl. Math. Comput. 167 561 | | [39] | Miller S K and Ross B 1993 An Introduction to the Fractional Calculus and Fractional Differential Equation (New York: John Wiley & Sons) | | [40] | El-Shewy E K 2005 Chaos Solitons Fractals 26 1073 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
