Ghany, H. A.; Fathallah, A. Exact solutions for KdV-Burger equations with an application of white-noise analysis. (English) Zbl 1248.60079 Int. J. Pure Appl. Math. 78, No. 1, 17-28 (2012). Summary: We will give exact solutions of the variable coefficient KdV-Burger equations \[ u_t + \alpha(t)uu_x + \beta (t)u_{xx} + \gamma (t)u_{xxx}=0, \] where \(\alpha(t), \beta(t)\) and \(\gamma(t)\) are bounded measurable or integrable functions on \(\mathbb{R}_+\). Moreover, using the Hermite transform and the homogeneous balance principle, the white noise functional solutions for the Wick-type stochastic KdV-Burger equations are explicitly obtained. Cited in 5 Documents MSC: 60H30 Applications of stochastic analysis (to PDEs, etc.) 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 35R60 PDEs with randomness, stochastic partial differential equations Keywords:modified tanh-coth method; KdV-burger equation; Hermite transform; Wick-type stochastic nonlinear differential equations; white noise PDFBibTeX XMLCite \textit{H. A. Ghany} and \textit{A. Fathallah}, Int. J. Pure Appl. Math. 78, No. 1, 17--28 (2012; Zbl 1248.60079) Full Text: Link