Power-Logistic Fronts in a Lossy Nonlinear Transmission Line
Abstract
We consider a lossy transmission line with a nonlinear voltage--charge relation. In the framework of the inverse-design method, starting from a prescribed monotonic front profile, we determine exactly the voltage--charge relation in the transmission line where the front propagates and the squared local sound speed. The latter plays an important role in our analysis, determining the admissibility conditions for the front. We specifically consider fronts with the power-logistic profile, including its hyperbolic-tangent special case. All physically admissible fronts of this form are shocks rather than kinks. For such shocks, the voltage--charge relation and the squared local sound speed--charge relation are expressed in terms of the lower incomplete beta function. We formulate the modified inverse-design method to calculate the profile of a shock propagating in the transmission line with a prescribed voltage--charge relation. We examine the local spectral properties of the front propagating in the transmission line in terms of the original partial differential equations and show that the short-wavelength perturbation modes are damped. The kink--shock distinction obtained from the mechanical analogy is independently confirmed through the long-wavelength characteristic analysis.
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BibTeX
@misc{kogan2026powerlogistic,
title = {{Power-Logistic Fronts in a Lossy Nonlinear Transmission Line}},
author = {Eugene Kogan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.00723},
eprint = {2608.00723},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.00723},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Power-Logistic Fronts in a Lossy Nonlinear Transmission Line
AU - Eugene Kogan
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2608.00723
UR - https://arxiv.org/abs/2608.00723
AB - We consider a lossy transmission line with a nonlinear voltage--charge relation. In the framework of the inverse-design method, starting from a prescribed monotonic front profile, we determine exactly the voltage--charge relation in the transmission line where the front propagates and the squared local sound speed. The latter plays an important role in our analysis, determining the admissibility conditions for the front. We specifically consider fronts with the power-logistic profile, including its hyperbolic-tangent special case. All physically admissible fronts of this form are shocks rather than kinks. For such shocks, the voltage--charge relation and the squared local sound speed--charge relation are expressed in terms of the lower incomplete beta function. We formulate the modified inverse-design method to calculate the profile of a shock propagating in the transmission line with a prescribed voltage--charge relation. We examine the local spectral properties of the front propagating in the transmission line in terms of the original partial differential equations and show that the short-wavelength perturbation modes are damped. The kink--shock distinction obtained from the mechanical analogy is independently confirmed through the long-wavelength characteristic analysis.
ER -