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 e...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.展开更多
In this paper, the Wick-type stochastic mKdV equation is researched. Many Wick-type stochastic solitonlike solutions are given via Hermite transformation and further generalized projective Riccati equation method.
文摘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.
基金国家重点基础研究发展计划(973计划)，the National Natural Science Foundation of China under
文摘In this paper, the Wick-type stochastic mKdV equation is researched. Many Wick-type stochastic solitonlike solutions are given via Hermite transformation and further generalized projective Riccati equation method.
