Further physical research about soliton structures and phase portraits in nonlinear fractional electrical transmission line model

Abstract

This paper presents several novel contributions in the field of nonlinear fractional low-pass electrical transmission line model (NFLETLM). Firstly, using the modified (G′G2)-expansion method and the extended modified Jacobi elliptic expansion method, we discovered new and accurate solutions for NFLETLM, which have not been reported in the existing literature (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). These solutions, denoted as U3,U4,U7,U8,U9,U10,U13,U14 and UJ1,UJ2,UJ3,UJ4 represent novel contributions to the fields. Secondly, by utilizing computer simulations, we observed various intriguing phenomena in the wave solution graphs, such as anti-kink waves, periodic waves, intense singular periodic waves, bright singular wave solutions, multi-periodic waves, intense double periodic waves, and alternating patterns of light and shade waves. These findings shed light on previously unexplored aspects of the problem. Thirdly, through an extensive study on the newly discovered solutions, we provided a comprehensive understanding of the solitons inherent in the NFLETLM, including comparison with other derivative solutions. Our conformable fractional derivative solutions showed similarities to beta derivative solutions, distinguishing them from Riemann–Liouville derivative solutions. Lastly, we explored the phase portrait, bifurcation analysis, sensitivity, and potential chaotic behaviors of the NFLETLM, which have not been addressed in previous works (Tala-Tcbuc et al. 2014; Nuruzzaman et al. 2021). This innovative contribution expands our understanding of the NFLETLM model and uncovers new dynamics and phenomena.

Keywords

• Fraction order
• Nonlinear electrical transmission
• Jacobi elliptic function
• Exact solutions
• Bifurcation
• Chaos behaviors