Wick型随机mKdV方程带多参量的广义的有理指数函数解.pdf

Advances in Applied Mathematics 应用数学进展, 2017, 6(9), 1056-1062 Published Online December 2017 in Hans. /journal/aam /10.12677/aam.2017.69128 A Generalized Rational-Exponent Function Solution with Multi-Parameter for Wick-Type Stochastic mKdV Equation Qing Liu Institute of Optics and Electronics, School of Engineering, Lishui University, Lishui Zhejiang nd th th Received: Nov. 22 , 2017; accepted: Dec. 4 , 2017; published: Dec. 11 , 2017 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 parame- ters 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. Keywords Wick-Type Stochastic mKdV Equation, Rational-Exponent Function Solution, White Noise, Hermite Transformation Wick型随机mKdV方程带多参量的广义的有理 指数函数解 留 庆 丽水学院工学院光电研究所，浙江 丽水 收稿日期：2017年11月22 日；录用日期：2017年12月4 日；发布日期：2017年12月11 日 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. DOI: 10.12677/aam.2017.69128 留庆 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