Baseband Modulational Instability and Manifestation of Breather and Super Rogue Wave Phenomena in Modified Noguchi Electrical Transmission Line

In this paper, we report the emergence of breather and super rogue waves in a modified Noguchi electrical transmission line and demonstrate that both phenomena arise from baseband modulational instability. We then systematically examine the influence of three key parameters and time that appear in the solutions, on the structure and behavior of breathers and super rogue waves, how they control waveform amplitude, localization, and intensity. We also explore the intricate dynamics of wave propagation in nonlinear electrical line. Our findings provide valuable insights into the role of network parameters, such as inductances, capacitances, and nonlinear coefficients, in shaping wave behavior, offering not only practical guidelines for the design, stability, and experimental investigation of electrical transmission systems but also provides practical approaches for controlling and managing breather and super rogue wave phenomena in the transmission lines.