Abstract
Weakly nonlinear long waves are investigated on a coupled transmission line which consists of two L C ladder lines connected by intermediary capacitors. It is found that there may exist two possible modes (fast and slow) on such a coupled line. Each mode is governed, in general, by a respective Korteweg-de Vries (K-dV) equation. For the slow mode, however, the coefficient of the nonlinear term in K-dV equation does vanish when characteristic parameters take critical values. The slow mode is then described by an equation of 31 combined form of K-dV and modified K-dV equation, which admits shock wave solution in addition to the usual solitary wave solution. These results show that there is a strong analogy between the present waves and long gravity waves can a two-layer fluid.
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