Energy transport and interaction dynamics of localized waves in nonlinear dispersive systems

Energy transport in nonlinear wave systems plays an important role in many physical processes where localized waves transfer energy through dispersive media. The objective of this study was to investigate the mechanisms of energy transport in a nonlinear wave system and to determine how nonlinear interactions influence the propagation and interaction of localized wave packets. Experiments were performed using a nonlinear electrical transmission line designed to generate and propagate controlled wave pulses. Temporal waveforms were measured at multiple positions along the transmission medium to analyze propagation dynamics and wave–wave interactions. In parallel, numerical simulations based on a nonlinear wave equation were conducted to reproduce and interpret the observed behavior. The experimental results demonstrated that localized wave packets propagate with nearly constant velocity and maintain a stable waveform during propagation. The initial pulse amplitude decreased only slightly from approximately 8.2 V to 7.5 V over the measured propagation distance, while the pulse width remained within the range of 42–45 ns. Interaction experiments showed that two wave packets temporarily form a combined structure with a peak amplitude of about 13.4 V during collision, after which the pulses recover their original shapes and continue propagating independently. Analysis of the spatial energy distribution revealed that wave energy remains strongly localized and moves through the system without significant dispersive spreading. Numerical simulations reproduced the experimentally observed propagation velocity, pulse stability, and interaction dynamics. These results confirm that energy transport in nonlinear dispersive media occurs through stable localized wave packets whose structure is maintained by the balance between nonlinear self-interaction and dispersion. The findings provide experimental and numerical evidence of efficient energy transfer mechanisms in nonlinear wave systems and contribute to the understanding of soliton-based energy transport in physical media.