Bifurcation features, chaos, and coherent structures for one-dimensional nonlinear electrical transmission line

This paper intends to investigate the bifurcation features with chaos and nonlinear coherent structures for the voltage wave propagation by developing a Hamiltonian dynamical system from the leading equations for the nonlinear electrical transmission lines (NLETLs). The effort is confirmed by the novel soliton, and other solutions for one-dimensional NLETL by considering the cubic-quintic-septic nonlinear medium. Using the extended simplest equation method (ESEM), various types of wave (e.g., bright/dark soliton and shocks, singular soliton, and periodic) solutions are determined. Subsequently, the dynamical theory is employed for analyzing the stability of NLETL. It is observed that the traveling wave reference velocity is incorporated various types of solitary waves that act similarly to the bifurcation parameters. The critical velocity of the traveling waves is also generated a pitchfork bifurcation. The existence of chaos in NLETL is justified by applying the Lyapunov spectrum theory.