[1] Chen Bin,. Auto-Bäcklund transformation and exact solutionsof Wick-type stochastic Burgers equation [J]. Journal of Southeast University (English Edition), 2005, 21 (4): 513-516. [doi:10.3969/j.issn.1003-7985.2005.04.028]

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Auto-Bäcklund transformation and exact solutionsof Wick-type stochastic Burgers equation()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

21

Issue:

2005 4

Page:

513-516

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2005-12-30

Info

Title:

Auto-Bäcklund transformation and exact solutionsof Wick-type stochastic Burgers equation

Author(s):

Chen Bin

Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, China

Keywords:

Wick-type stochastic Burgers equation;  auto-Bä cklund transformation;  stochastic soliton solution;  white noise;  Hermite transform;  homogeneous balance principle

PACS:

O211.6;O175.2

DOI:

10.3969/j.issn.1003-7985.2005.04.028

Abstract:

Burgers equation in random environment is studied.In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W(t)=(·overB)_t, where B_t is a Brown motion.The auto-Bäcklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform.The generalization of the Wick-type stochastic Burgers equation is also studied.

References:

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[3] Chen B, Xie Y C.An auto-Backlund transformation and exact solutions of stochastic Wick-type Sawada-Kotera equations[J].Chaos, Solitons & Fractals, 2004, 23(1):281-287.
[4] Chen B, Xie Y C.Exact solutions for Wick-type stochastic coupled Kadomtsev-Petviashvili equations[J].J Phys A:Math Gen, 2005, 38(4):815-822.
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[8] Xie Y C.Positonic solutions for Wick-type stochastic KdV equations[J].Chaos, Solitons & Fractals, 2004, 20(2):337-342.
[9] Xie Y C.Exact solutions of the Wick-type stochastic Kadomtsev-Petviashvili equations[J].Chaos, Solitons & Fractals, 2004, 21(2):473-480.
[10] Xie Y C.An auto-Backlund transformation and exact solutions for Wick-type stochastic generalized KdV equations[J].J Phys A:Math Gen, 2004, 37(19):5229-5236.
[11] Xie Y C.Exact solutions for Wick-type stochastic coupled KdV equations[J].Phys Lett A, 2004, 327(2, 3):174-179.
[12] Holden H, Øksendal B, UbØe J, et al.Stochastic partial differential equations:a modeling, white noise functional approach[M].Boston:Birhkäuser, 1996. 141-187.
[13] Wang M L.Exact solutions for a compound KdV-Burgers equation[J].Phys Lett A, 1996, 213(5, 6):279-287.

Memo

Memo:

Biography: Chen Bin(1965—), female, master, associate professor, bchen@xznu.edu.cn.

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