Soliton propagation and dynamical insights in lossy nonlinear transmission lines

In this article, we explore the solitary wave solutions and dynamical analysis of the lossy nonlinear transmission line model (NLTLM). The NLTLM is defined as a structure through which short-duration pulses, known as electrical solitons, can be generated and propagated. Conservation laws are computed using the multiplier approach. Soliton solutions are obtained using the generalized logistic equation and the tanh method. We derive exponential, trigonometric, and algebraic types of soliton solutions. These results are valuable for modeling signal concentrations in nonlinear transmission lines (NLTLs). The associated planar dynamical system, formulated via Galilean transformation with appropriate mathematical models and parameters, enhances our understanding of the problem. Additionally, we investigate the system’s dynamic behavior under a perturbing force, identifying chaotic patterns through tools such as the return map, fractal dimension, basin attractors, power spectrum, and Lyapunov exponents. The parameters of the transmission line significantly influence the original form of the soliton.