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Exact solutions for KdV-Burger equations with an application of white-noise analysis. (English) Zbl 1248.60079

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.

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
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