Solitary waves, bifurcation, chaos, sensitivity, and multistability of electrical transmission line model

This research explores the (2+1)-D nonlinear electrical transmission line equation (NLETLE), highlighting its unique localized wave solutions and the interactions that arise from them. Through the application of a novel multivariate generalized exponential differential function technique and generalized logistic equation approach, we have successfully generated a diverse array of new structures, particularly characterized by bright soliton, bright-singular soliton, kink soliton, and periodic waveforms. These solutions play a crucial role in demonstrating the complex structure and varied dynamics that are characteristic of nonlinear systems in higher dimensions. To achieve a comprehensive understanding, we depict these solutions using 3D surface density plots and line graphs. Additionally, we analyze the dynamic behavior of the system through bifurcation analysis, which is graphically represented by phase portraits. Subsequently, we incorporate periodic functions into the dynamical system to investigate the nonlinear properties of the dynamical system, in order to uncover its chaotic behavior, utilizing concepts derived from the theory of chaos. The observation and confirmation of chaotic behavior are achieved by employing a range of chaos detection tools. In addition, we conduct a sensitivity analysis to determine how minor modifications in the system affect its overall behavior, which in turn provides greater insight into its robustness and ability to respond to perturbations. By varying the initial conditions, we analyze multistability, which highlights the system's ability to display multiple stable states influenced by choosing suitable parametric values. The results acquired from this research are new and significant for the continued exploration of the (2+1)-D NLETLE, offering direction for future scholars.