Research on nonlinear electric transmission model based on Hamiltonian structure with numerical accuracy analysis

This paper employs the extended hyperbolic tangent function method and the Runge–Kutta–Nyström (RKN) method to analyze a nonlinear fractional-order electrical transmission line model, revealing the impact of fractional-order derivatives (α) and free parameters (ν,β,a) on voltage soliton dynamics. Key results show that increasing α from 0.25 to 0.75 enhances soliton amplitude by 30–50 percent and sharpens waveform profiles, reflecting the system’s memory-dependent behavior (Figs. 2–7). The RKN method achieves high-precision numerical solutions with a maximum absolute error of 3×10−7 in [0.1,2]×[1,2] (Table 1), outperforming traditional methods. Hamiltonian system analysis uncovers diverse equilibrium states (centers, saddle points) and chaotic responses to noise amplitude (f) and frequency (ω0) (Figs. 18–21). Parameter sensitivity studies demonstrate that ν and β modulate soliton peak positions, while a affects wave velocity (Figs. 8–9). The study also compares solutions under modified Riemann–Liouville and beta derivatives, highlighting their distinct physical interpretations (Fig. 11). These findings provide a theoretical foundation for optimizing transmission line design and controlling nonlinear dynamics in electrical systems.