Propagation of Waves Through Anharmonic Defects

Dynamical systems with localized anharmonicity are generally described by Volterra Integro-Differrential Equations, which in cases of dispersionless infinite harmonic parts reduce to differential equations and in cases of finite dispersionless harmonic parts to delayed differential equations. The simplest examples of all three cases are given. Specific results for the surface atom and for an anharmonic stub resonator are presented. Simplified characteristics of chaotic motion are introduced. Typical memory kernels for integro differential equations in non-dispersionless media are derived.