Exact solutions for a Wick-type stochastic reaction Duffing equation

摘要

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(r) 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.