Analytic solutions for shock waves in nonlinear transmission lines show new approximations in lossless systems, indicating advances in wave dynamics.
In the first part of the paper we obtain the analytic solution for the profile of a shock wave in a nonlinear lossy transmission line, constructed from the inductors, the capacitors and the resistors. both the charge of a capacitor and a current through the inductor are obtained as the functions of the time and space coordinate. In the second part of the paper we formulate the simple wave approximation for the nonlinear lossless transmission line.
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E. Kogan (2025) studied this question.
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