Exact Solutions of a Functional Equation Arising in Nonlinear Wave Propagation

Abstract

The time-periodic response of a gas-filled tube to a reciprocating piston is described in terms of the solution to a functional difference equation. When both the gas velocity and acceleration remain small, this functional equation may be approximated by a nonlinear ordinary differential equation. In this paper we demonstrate, through three classes of exact solutions, when and in what sense the differential equation is a good approximation to the functional equation.