In this paper, the solution to semi-linear hyperbolic systems of the form A(x, t)u_t + B(x,t)u_{x +} c(x, t)u = f(x,t,u) in Ωx(0,∞) with u(x,0) = φ (x) is given. We apply this solution approached to establish the solution representation for any isentropic fluid flow.

KEYWORDS: Hyperbolic Systems, Characteristic curves, eigenvalues, eigenvectors, isentropic fluid.