IJPAM: Volume 78, No. 1 (2012)

EXACT SOLUTIONS FOR KDV-BURGER
EQUATIONS WITH AN APPLICATION OF
WHITE-NOISE ANALYSIS

Hossam A. Ghany$^{1,2}$, Ashraf Fathallah$^3$
$^1$Department of Mathematics
Helwan University
Cairo, EGYPT
$^2$Department of Mathematics
Taif University
Taif, KINGDOM OF SAUDI ARABIA
$^{3}$Department of Mathematics
Misr International University
Cairo, EGYPT


Abstract. In this paper we will give exact solutions of the variable coefficient KdV-Burger equations u_t+(t)uu_x+(t)u_xx+(t)u_xxx=0, where $\alpha(t)$, $\beta(t)$ and $\gamma(t)$ are bounded measurable or integrable functions on $\Bbb{R}_+$. 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.

Received: December 26, 2011

AMS Subject Classification: 60H30, 60H15, 35R60

Key Words and Phrases: modified tanh-coth method, KdV-Burger equation, Hermite transform, Wick-type stochastic nonlinear differential equations, white noise

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 78
Issue: 1