Shock Waves in Nonlinear Transmission Lines

In the first half of the article, interaction between the small amplitude travelling waves (“sound”) and the shock waves in the transmission line containing both nonlinear capacitors and nonlinear inductors is considered. Herein, the “sound” wave coefficient of reflection from (coefficient of transmission through) the shock wave is calculated. These coefficients are expressed in terms of the speeds of the “sound” waves relative to the shock and the wave impedances. In the second half of the article, the dissipation in the system is explicitly included into consideration, introducing Ohmic resistors shunting the inductors and also in series with the capacitors. This allows us to justify the conditions on the shocks, postulated in the first half of the article. This also allows us to describe the shocks as physical objects of finite width and study their profiles, same as the profiles of the waves closely connected with the shocks—the kinks. The profiles of the latter, and in some particular cases, the profiles of the former are obtained in terms of elementary functions.