Journal
APPLIED MATHEMATICAL MODELLING
Volume 39, Issue 23-24, Pages 7420-7426Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.03.019
Keywords
Wick-type stochastic reaction Duffing equation; White-noise theory; Exact solutions
Funding
- Zhejiang Provincial Natural Science Foundation of China [LY13F050006]
- National Natural Science Foundation of China [11375007]
- Scientific Research and Developed Fund of Zhejiang A F University [2014FR020]
- Foundation of New Century 151 Talent Engineering of Zhejiang Province of China
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We study a Wick-type stochastic reaction Duffing equation, and obtain some new exact solutions with the help of the white-noise theory and the exact solution of the Riccati equation. From exact solution, it is found that the amplitude and pulse width are not influenced by system functions h(1) (t), h(2)(t) and the Brownian motion B(t). We can also find that the functions h(1) (t), h(2) (t) and B(t) are the primary influential factors for the variation of the solitary wave group velocity. Based on these exact solutions, we also discuss the influence of stochastic effect for chaotic system on dynamical behaviors. These exact solutions, especially the solitonic solutions, might help us to better understand the physical stochastic mechanisms in the mechanical problems. (C) 2015 Elsevier Inc. All rights reserved.
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