一类随机KdV方程组的白噪声泛函解

Exact Solutions for Wick Type Stochastic Generalized KdV Equations

该文研究了一类随机Wick-类型KdV方程,并在Kondratiev分布空间(S)-1中利用Hermite变换转化成广义变系数KdV方程组.利用齐次平衡原则,推导出广义变系数KdV方程组的Backlund变换,求出了该方程组的若干精确解.然后通过Hermite变换的逆变换求出Wick-类型的随机广义KdV方程组的白色噪声泛函解.

In the paper,we studied a class of stochastic Wick type KdV equations and used Hermite transformation to change the equation into a generalized variable coefficient KdV equations in the Kondratiev distribution space(S)-1.By using the principle of homogeneous equilibrium,the Bǎcklund transformation of generalized variable coefficients KdV equations was derived.Then,some exact solutions of the equations were obtained.And then by Hermite transform inverse transform to find out white noise functional solutions for Wick types of stochastic generalized KdV equations.