Transmission of Positons in a Modified Noguchi Electrical Transmission Line

Abstract

In previous studies, the propagation of localized pulses (solitons, rogue waves and breathers) in electrical transmission lines has been studied. In this work, we extend this study to explore the transmission of positon solutions or positons in the modified Noguchi electrical transmission line model. By converting the circuit equations into the nonlinear Schr\"odinger equation, we identify positons, a special type of solution with algebraic decay and oscillatory patterns. Unlike solitons, which are used for stable energy transmission, positons provide persistent energy localization and controlled spreading over long distances. We consider second-order and third-order positon solutions and examine their transmission behaviour in electrical lines. We show that over long times, the amplitude and width of both second- and third-order positons remain largely unaffected, indicating stable transmission. We also analyze what are the parameters affect the amplitude and localization of this kind of waves. Our investigations reveal that the amplitude and localization of positons are significantly influenced by the parameter $\epsilon$ that appear in the solution. Our findings have practical implications for improving energy transmission in electrical systems, where the management of wave localization and dispersion is crucial.