Abstract
In this paper we study the propagation of acoustic waves in a one-dimensional system with nonstationary chaotic elasticity distribution. The elasticity distribution is assumed to have a power spectrum S(f) ~ 1/f(2B-3)/(B-1) for B ≥ 1.5. By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the Lyapunov exponent. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of weak localized acoustic waves for high degree of correlations (B > 2).
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