|
|
The fractional coupled KdV equations:Exact solutions and white noise functional approach |
Hossam A. Ghanya c, A. S. Okb El Babb, A. M. Zabelc, Abd-Allah Hyderd |
a Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia; b Department of Mathematics, Faculty of Science, Al-Azhar University, Cairo, Egypt; c Department of Mathematics, Faculty of Industrial Education, Helwan University, Cairo, Egypt; d Department of Physics and Mathematics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt |
|
|
Abstract Variable coefficients and Wick-type stochastic fractional coupled KdV equations are investigated. By using the modified fractional sub-equation method, Hermite transform, and white noise theory the exact travelling wave solutions and white noise functional solutions are obtained, including the generalized exponential, hyperbolic, and trigonometric types.
|
Received: 21 October 2012
Revised: 07 March 2013
Accepted manuscript online:
|
PACS:
|
05.40.-a
|
(Fluctuation phenomena, random processes, noise, and Brownian motion)
|
|
02.30.Jr
|
(Partial differential equations)
|
|
Corresponding Authors:
Hossam A. Ghany
E-mail: h.abdelghany@yahoo.com
|
Cite this article:
Hossam A. Ghany, A. S. Okb El Bab, A. M. Zabel, Abd-Allah Hyder The fractional coupled KdV equations:Exact solutions and white noise functional approach 2013 Chin. Phys. B 22 080501
|
[1] |
Holden H, Øsendal B, Ubøe J and Zhang T 1996 Stochastic Partial Differential Equations (Birhkäuser: Basel) pp. 159-163
|
[2] |
Sweilam N H, Khader M M and Al-Bar 2007 Phys. Lett. A 371 26
|
[3] |
Daftardar-Gejji V and Jafari H 2007 Appl. Math. Comput. 189 541
|
[4] |
Daftardar-Gejji V and Bhalekar S 2008 Appl. Math. Comput. 202 113
|
[5] |
Golbabai A and Sayevand K 2010 Nonlinear Sci. Lett. A 1 147
|
[6] |
Golbabai A and Sayevand K 2011 Comput. Math. Appl. 62 1003
|
[7] |
Li B A and Wang M L 2005 Chin. Phys. 14 1698
|
[8] |
Wang M L and Zhou Y B 2003 Phys. Lett. A 318 84
|
[9] |
Wang M L, Wang Y M and Zhang J L 2003 Chin. Phys. 12 1341
|
[10] |
Zhang J L, Ren D F and Wang M L 2003 Chin. Phys. 12 825
|
[11] |
Zhou Y B, Wang M L and Wang Y M 2003 Phys. Lett. A 308 31
|
[12] |
Li Z B and He H J 2010 Math. Comput. Appl. 15 970
|
[13] |
Wadati M J 1983 Phys. Soc. Jpn. 52 2642
|
[14] |
Xie Y C 2003 Phys. Lett. A 310 1617
|
[15] |
Xie Y C 2004 Chaos, Solitons and Fractals 20 33742
|
[16] |
Xie Y C 2004 J. Phys. A: Math. Gen. 37 522936
|
[17] |
Xie Y C 2004 Chaos, Solitons and Fractals 21 47380
|
[18] |
Chen B and Xie Y C 2005 J. Phys. A: Math. Gen. 38 81522
|
[19] |
Chen B and Xie Y C 2005 Chaos, Solitons and Fractals 23 2817
|
[20] |
Chen B and Xie Y C 2007 J. Comput. Appl. Math. 203 24963
|
[21] |
Ghany H A 2011 Chin. J. Phys. 49 926
|
[22] |
Ghany H A and Saad M 2012 Chin. J. Phys. 50 618
|
[23] |
Hou G L and Liu J C 2010 Chin. Phys. B 19 110305
|
[24] |
Tian N S, Xia Z Q and Wei C M 2005 Acta Phys. Sin. 54 2463 (in Chinese)
|
[25] |
Grimshaw R and Christodoulides P 2010 Physica D 239 635
|
[26] |
Momani S 2005 Math. Comp. Simul. 70 110
|
[27] |
Oldham K B and Spanier J 1974 The Fractional Calculus (New York: Academic Press)
|
[28] |
Jumarie G 2006 Comput. Math. Appl. 51 1367
|
[29] |
Odibat Z and Momani S 2008 Chaos, Solitons and Fractals 36 167
|
[30] |
Zhang S, Zong Q A, Liu D and Gao Q 2010 Communications in Fractional Calculus 1 48
|
[31] |
Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
|
[32] |
He J H 2000 Int. J. Nonlinear Mech. 35 37
|
[33] |
He J H, Elagan S K and Li Z B 2012 Phys. Lett. A 376 257
|
[34] |
Ghany H A accepted by Chin. J. Phys. 51
|
[35] |
Ghany H A and Hyder A 2013 J. Compt. Anal. Appl. 15 1332
|
[36] |
Fan E G 2002 Phys. Lett. A 300 243
|
[37] |
Fan E G 2003 J. Phys. A: Math. Gen. 36 7009
|
[38] |
Fan E G and Dai H 2003 Comput. Phys. Commun. 153 17
|
[39] |
Fan E G and Hon Y 2003 Chaos, Solitons and Fractals 15 559
|
[40] |
He J H 1999 Comput. Methods Appl. Mech. Engrg. 178 257
|
[41] |
He J H 2012 Abstract and Applied Analysis 2012 916793
|
[42] |
He J H and Wu X H 2006 Chaos, Solitons and Fractals 30 700
|
[43] |
Wu X H and He J H 2007 Comput. Math. Appl. 54 966
|
[44] |
Benth E and Gjerde J 1998 Potential Anal. 2 179
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|