Asymptotic behaviour of collisionless shock in nonlinear LC circuit

Asymptotic property of collisionless shock has been examined experimentally using a nonlinear LC circuit which simulates the Toda lattice. The shock front velocity depends on the magnitude of a discontinuity as a collisional shock, but the collisionless shock is not stationary. That is, soliton like peaks are generated behind the shock front as an initial step voltage propagates in the circuit. The time interval between these peaks increases logarithmically in time but decreases in proportion to square root of an initial amplitude. The results are qualitatively explained by a solution of Korteweg-de Vries equation. (author)