The Evolution of a Self-Sustained Oscillation in a Nonlinear Continuous System

TLDR: In this paper, a gas filled tube has a pressure sensitive heat source at the center, while energy is allowed to radiate from the ends, and the small amplitude disturbance in the pipe is represented as the superposition of two simple waves traveling in opposite directions.

Abstract: : A gas filled tube has a pressure sensitive heat source at the center, while energy is allowed to radiate from the ends. For a sufficiently large feedback coefficient the system is linearly unstable. Within the nonlinear theory, the self-excited oscillation initially grows until a shock forms. The shock acts as a dissipative mechanism so that a balance is achieved and ultimately a time periodic state is reached. The small amplitude disturbance in the pipe is represented as the superposition of two simple waves traveling in opposite directions, and without interaction. Based on this representation the problem reduces to solving a nonlinear difference equation. (Author)