Abundant solutions of Wick-type stochastic fractional 2D KdV equations

doi:10.1088/1674-1056/23/6/060503

中国物理B ›› 2014, Vol. 23 ›› Issue (6): 60503-060503.doi: 10.1088/1674-1056/23/6/060503

Abundant solutions of Wick-type stochastic fractional 2D KdV equations

Hossam A. Ghany^{a b}, Abd-Allah Hyder^c

a Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia;
b Department of Mathematics, Helwan University, Cairo, Egypt;
c Department of Engineering Physics and Mathematics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt

收稿日期:2013-11-26 修回日期:2013-12-23 出版日期:2014-06-15 发布日期:2014-06-15

Abundant solutions of Wick-type stochastic fractional 2D KdV equations

Hossam A. Ghany^{a b}, Abd-Allah Hyder^c

a Department of Mathematics, Faculty of Science, Taif University, Taif, Saudi Arabia;
b Department of Mathematics, Helwan University, Cairo, Egypt;
c Department of Engineering Physics and Mathematics, Faculty of Engineering, Al-Azhar University, Cairo, Egypt

Received:2013-11-26 Revised:2013-12-23 Online:2014-06-15 Published:2014-06-15
Contact: Hossam A. Ghany, Abd-Allah Hyder E-mail:h.abdelghany@yahoo.com;abdallah_hyder@yahoo.com

摘要/Abstract

摘要： A modified fractional sub-equation method is applied to Wick-type stochastic fractional two-dimensional (2D) KdV equations. With the help of a Hermit transform, we obtain a new set of exact stochastic solutions to Wick-type stochastic fractional 2D KdV equations in the white noise space. These solutions include exponential decay wave solutions, soliton wave solutions, and periodic wave solutions. Two examples are explicitly given to illustrate our approach.

关键词: 2D KdV equations, fractional calculus, white noise, Hermite transform

Abstract: A modified fractional sub-equation method is applied to Wick-type stochastic fractional two-dimensional (2D) KdV equations. With the help of a Hermit transform, we obtain a new set of exact stochastic solutions to Wick-type stochastic fractional 2D KdV equations in the white noise space. These solutions include exponential decay wave solutions, soliton wave solutions, and periodic wave solutions. Two examples are explicitly given to illustrate our approach.

Key words: 2D 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, Abd-Allah Hyder. Abundant solutions of Wick-type stochastic fractional 2D KdV equations[J]. 中国物理B, 2014, 23(6): 60503-060503.

Hossam A. Ghany, Abd-Allah Hyder. Abundant solutions of Wick-type stochastic fractional 2D KdV equations[J]. Chin. Phys. B, 2014, 23(6): 60503-060503.

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Abundant solutions of Wick-type stochastic fractional 2D KdV equations

Abundant solutions of Wick-type stochastic fractional 2D KdV equations

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