The fractional coupled KdV equations：Exact solutions and white noise functional approach

doi:10.1088/1674-1056/22/8/080501

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80501-080501.doi: 10.1088/1674-1056/22/8/080501

The fractional coupled KdV equations：Exact solutions and white noise functional approach

Hossam A. Ghany^{a c}, A. S. Okb El Bab^b, A. M. Zabel^c, Abd-Allah Hyder^d

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

收稿日期:2012-10-21 修回日期:2013-03-07 出版日期:2013-06-27 发布日期:2013-06-27

The fractional coupled KdV equations：Exact solutions and white noise functional approach

Hossam A. Ghany^{a c}, A. S. Okb El Bab^b, A. M. Zabel^c, Abd-Allah Hyder^d

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

Received:2012-10-21 Revised:2013-03-07 Online:2013-06-27 Published:2013-06-27
Contact: Hossam A. Ghany E-mail:h.abdelghany@yahoo.com

摘要/Abstract

摘要： 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.

关键词: coupled KdV equations, fractional calculus, white noise, Hermite transform

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.

Key words: coupled KdV equations, fractional calculus, white noise, Hermite transform

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

02.30.Jr (Partial differential equations)

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[J]. 中国物理B, 2013, 22(8): 80501-080501.

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[J]. Chin. Phys. B, 2013, 22(8): 80501-080501.

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The fractional coupled KdV equations：Exact solutions and white noise functional approach

The fractional coupled KdV equations：Exact solutions and white noise functional approach

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