This study on Lossy Nonlinear Electrical Transmission Line Models (LNETLM) highlights several novel contributions: (1) Introducing the modified \(\left( \frac{G^{'}}{G^2}\right) \) -expansion method applied to LNETLM with a beta derivative, providing precise soliton solutions previously undocumented in the field; (2) Through extensive computer simulations, uncovering diverse wave phenomena such as bright, solitary, and parabolic solitons, alongside oscillatory singular waves, advancing the characterization of wave dynamics within LNETLM; (3) Contrasting conformable, M-truncated derivatives with the beta derivative, revealing the unique advantages of the beta derivative approach in modeling electrical transmission line systems; (4) Transforming the LNETLM equation into a Hamiltonian system, analyzing phase portraits, Chaos, and bifurcation phenomena, enhancing understanding of system dynamics and stability; (5) Expanding the knowledge frontier in lossy electrical transmission line models, with implications for theoretical understanding and practical applications in signal transmission and communication systems. In conclusion, this research underscores the potential of pulse-like solitons for enhancing data transmission rates in telecommunication systems. The insights gained pave the way for advancements in telecommunication technology, promising improved efficiency and performance.
