Auto-Bcklund transformation and exact solutions of Wick-type stochastic Burgers equation  

Wick型随机Burgers方程的自Bcklund变换和精确解(英文)

作　　者：陈彬[1] 

机构地区：[1]徐州师范大学数学系,徐州221116

出　　处：《Journal of Southeast University(English Edition)》2005年第4期513-516,共4页东南大学学报（英文版）

基　　金：TheNationalNaturalScienceFoundationofChina(No.10471120),theNaturalScienceFoundationofXuzhouNormalUniversity(No.04XLA15).

摘　　要：Burgers equation in random environment is studied. In order to give the exact solutions of random Burgers equation, we only consider the Wick-type stochastic Burgers equation which is the perturbation of the Burgers equation with variable coefficients by white noise W（t）=Bt, where Bt is a Brown motion. The auto-Baecklund transformation and stochastic soliton solutions of the Wick-type stochastic Burgers equation are shown by the homogeneous balance and Hermite transform. The generalization of the Wick-type stochastic Burgers equation is also studied.研究了随机环境中的Burgers方程.为了给出随机Burgers方程的精确解,只讨论变系数Burgers方程的系数经白噪声W(t)=B·(t)扰动所得的Wick型随机Burgers方程(B(t)是Brown运动),利用齐次平衡原理和Hermite变换给出了Wick型随机Burgers方程的自Bcklund变换和随机孤立子解的精确表达式,同时也研究了一般情形的Wick型随机Burgers方程.

关 键 词：Wick-type stochastic Burgers equation auto-Baecklund transformation stochastic soliton solution white noise Hermite transform homogeneous balance principle 

分 类 号：O211.6[理学—概率论与数理统计] O175.2[理学—数学]