A nonlinear electrical lattice provides an effective platform for observing soliton propagation and energy localization in dispersive media. This work analyzes the nonlinear dynamics of the ( \(1+1\) )-dimensional Salerno equation, which governs discrete electrical lattices with nonlinear dispersion. Using the modified Sardar sub-equation method (MSSEM), we derive exact soliton solutions, including bright, dark, kink, and combo types, that characterize signal transmission and localization in nonlinear systems. Beyond solution construction, we present a comprehensive bifurcation analysis to uncover different dynamical regimes that demarcate transitions between stability, instability, and periodicity. To further explore the nonlinear properties of the system, we carry out an exhaustive chaotic analysis supported by return maps, Poincaré sections, Lyapunov exponents, and power spectra, which demonstrate the sensitive dependence on distinct initial conditions and the emergence of strange attractors in phase space. This integrated soliton-chaos framework provides a comprehensive mathematical basis for discrete electrical lattices, with implications for robust signal propagation, chaotic signal generation, and energy-efficient switching in sophisticated electrical and optical communication networks.
