Int. J. Contemp. Math. Sciences, Vol. 3, 2008, no. 15, 745 - 751 Exact Solutions of Some Hyperbolic Equations with Initial Conditions J. Biazar 1 and S. Bozorgi Department of Mathematics, Faculty of Sciences University of Guilan, P.O. Box 1914, Rasht, Iran biazar@guilan.ac.ir Samira.Bozorgi@gmail.com Abstract Adomian decomposition method has been applied to solve many functional equations so far. In this article, we have used this method to solve some hyperbolic equations, Cuachy problems, with initial condi- tions. Keywords: Adomian decomposition method; Hyperbolic equations; Cauchy problems 1 Introduction Analytical methods commonly used for solving hyperbolic equations are very restricted and can be used in very special cases. Adomian decomposition method has a useful feature in that it provides the solution in a rapid convergent power series with elegantly computable conver- gence of the solution. The decomposition method has proven to be very effective and results in con- siderable savings in computation time. In this work we focus our study to hyperbolic equations. These equations can be written in the form a 11 u tt +2a 12 u tx + a 22 u xx + b 1 u t + b 2 u x + cu = f where a 2 12 - a 11 a 22 > 0 (1) with initial condintions: u(x, 0) = f 0 (x) ∂u(x, 0) ∂t = f 1 (x) (2) 1 Corresponding author