Wick型随机mKdV方程带多参量的广义的有理指数函数解
A Generalized Rational-Exponent Function Solution with Multi-Parameter for Wick-Type Stochastic mKdV Equation
摘要: 借助Hermite变换、白噪声理论和Riccati方程的有理指数函数解，获得了Wick型随机mKdV方程带多参量的广义的有理指数函数解，借助这个解可以揭示出不同的Riccati方程约束条件下，不同的参量的变化对Wick型随机mKdV方程动力学行为产生的影响及变化规律。它为深入研究外部条件和内部因素对非线性随机模式行为产生的影响，提供了一种更加有效的方法。
Abstract: With the help of Hermite transformation, white noise theory and a rational-exponent function so-lution of Riccati equation, a rational-exponent function solution with multiple arbitrary parameters for Wick-type stochastic mKdV equation is obtained. From this rational-exponent function solution, the influence of variety of different parameters on the dynamics behavior of Wick-type stochastic mKdV equation by restricted Riccati equation is showed. It provides a more effective method, which can be used to investigate the influence of external conditions and internal factors on behavior of nonlinear stochastic dynamics model.
文章引用：留庆. Wick型随机mKdV方程带多参量的广义的有理指数函数解[J]. 应用数学进展, 2017, 6(9): 1056-1062. https://doi.org/10.12677/AAM.2017.69128

参考文献

[1] Wadati, M. (1983) Stochastic Korteweg-de Vries Equation. Journal of the Physical Society of Japan, 52, 2642-2648.
[Google Scholar] [CrossRef] 
[2] Wadati, M. and Akutsu, Y. (1984) Stochastic Korteweg-de Vries Equation with and without Damping. Journal of the Physical Society of Japan, 53, 3342-3350.
[Google Scholar] [CrossRef] 
[3] Wadati, M. (1990) Deformation of Solitons in Random Media. Journal of the Physical Society of Japan, 59, 4201-4203.
[Google Scholar] [CrossRef] 
[4] Bouard, A.D. and Debussche, A. (1998) On the Stochastic Korteweg-de Vries Equation. Journal of Functional Analysis, 154, 215-251.
[Google Scholar] [CrossRef] 
[5] Bouard, A.D. and Debussche, A. (1999) White Noise Driven Korteweg-de Vries Equation. Journal of Functional Analysis, 169, 532-258.
[Google Scholar] [CrossRef] 
[6] Debussche, A. and Printems, J. (1999) Numerical Simulation of the Stochastic Korteweg-de Vries Equation. Physica D, 134, 200-226.
[Google Scholar] [CrossRef] 
[7] Debussche, A. and Printems, J. (2001) Effect of a Localized Random Forcing Term on the Korteweg-de Vries Equation. Journal of Computational Analysis and Applications, 3, 183-206.
[Google Scholar] [CrossRef] 
[8] Konotop, V.V. and Vźquez, L. (1994) Nonlinear Random Waves. World Scientific, Singapore.
[Google Scholar] [CrossRef] 
[9] Printems, J. (1999) The Stochastic Korteweg-de Vries Equation in L(R2). Journal of Differential Equations, 153, 338-373.
[Google Scholar] [CrossRef] 
[10] Holden, H., Øsendal, B., Ubøe, J. and Zhang, T. (1996) Stochastic Partial Differential Equations. BirhKäuser, Boston.
[Google Scholar] [CrossRef] 
[11] Xie, Y.C. (2003) Exact Solutions for Stochastic KdV Equations. Physics Letters A, 310, 161-167.
[Google Scholar] [CrossRef] 
[12] Xie, Y.C. (2004) Exact Solutions of the Wick-Type Sto-chastic Kadomtsev-Petviashvili Equations. Chaos, Solitons & Fractals, 21, 473-480.
[Google Scholar] [CrossRef] 
[13] Wei, C.M., Ren, Y.H. and Xia, Z.Q. (2005) Symmetry Reduc-tions and Soliton-Like Solutions for Stochastic MKdV Equation. Chaos, Solitons & Fractals, 26, 1507-1513.
[Google Scholar] [CrossRef] 
[14] Dai, C.Q. and Chen, J.L. (2009) Exact Solutions of (2+1)-Dimensional Stochastic Broer-Kaup Equation. Physics Letters A, 373, 1218-1225.
[Google Scholar] [CrossRef] 
[15] Dai, C.Q. and Zhang, J.F. (2009) Application of He’s Exp-function Method to the Stochastic mKdV Equation. International Journal of Nonlinear Sciences and Numerical Simulation, 10, 675-680.
[Google Scholar] [CrossRef] 
[16] Liu, Q. (2006) Various Types of Exact Solutions for Sto-chastic mKdV Equation via a Modified Mapping Method. Europhysics Letters, 74, 377-383.
[Google Scholar] [CrossRef] 
[17] Liu, Q. (2007) Some Exact Solutions for Stochastic mKdV equa-tion. Chaos, Solitons & Fractals, 32, 1224-1230.
[Google Scholar] [CrossRef] 
[18] Liu, Q., Jia, D.L. and Wang, Z.H. (2010) Three Types of Exact Solutions to Wick-Type Generalized Stochastic Korteweg-de Vries Equation. Applied Mathematics and Computation, 215, 3495-3500.
[Google Scholar] [CrossRef] 
[19] Liu, Q., Lan, J.C., Wu, H.Y. and Wang, Z.H. (2010) A Series of Exact Solutions for (2+1)-Dimensional Wick-Type Stochastic Generalized Broer-Kaup System via a Modified Varia-ble-Coefficient Projective Riccati Equation Mapping Method. Applied Mathematics and Computation, 217, 629-638.
[Google Scholar] [CrossRef] 
[20] Liu, Q., Shen, S.Y. and Wang, Z.H. (2013) The Rational Solutions to a Generalized Riccati Equation and Their Application. International Journal of Modern Physics B, 27, 1350013.
[Google Scholar] [CrossRef] 

为你推荐