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

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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   

  1. 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. Ghanya c, A. S. Okb El Babb, A. M. Zabelc, Abd-Allah Hyderd   

  1. 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: 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)