Formation of a large-scale structure in a nonlinear dissipative system

Dynamic evolution of a small-scale structure to a large-scale structure is studied by a nonlinear dissipative LC ladder circuit. The circuit is descri bed by a Burgers equation in the lowest order. We confirmed that the observ ed propagation of a shock wave and the confluence of shock waves are well d escribed by the theory. A single hump wave is used to model a small-scale s tructure. When two single-hump waves with different amplitudes are applied to the circuit, they evolve into a large-scale structure in the course of p ropagation. Such a formation of a large-scale structure is unique in a nonl inear 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.