Formation of a Large-Scale Structure in a Nonlinear Dissipative System

Abstract

Dynamic evolution of a small-scale structure to a large-scale structure is studied by a nonlinear dissipative LC ladder circuit. The circuit is described by a Burgers equation in the lowest order. We confirmed that the observed propagation of a shock wave and the confluence of shock waves are well described by the theory. A single hump wave is used to model a small-scale structure. When two single-hump waves with different amplitudes are applied to the circuit, they evolve into a large-scale structure in the course of propagation. Such a formation of a large-scale structure is unique in a nonlinear dissipative system, while the nonlinear dispersive system is known to preserve the nature of small-scale structures even after their interaction as known for solitons.