Qualitative and quantitative fractional low-pass electrical transmission line model

Abstract

In this paper, the fractional low-pass electrical transmission line model is considered, whose fractional definition is defined by conformal fractional derivative. We first apply the complex fractional traveling wave transformation to the original equation, then the dynamic properties such as Hamiltonian and topological properties to its traveling wave system are presented via the complete discrimination system for polynomial method (CDSPM). From these results, the prior estimate of periodic solution and soliton solution is established. Moreover, quantitative results of all traveling wave solutions are also given. To the best of our knowledge, this is the first time that the Hamiltonian is constructed to this model, and all single traveling wave solutions are obtained.

Keywords

• Low-pass electrical transmission line
• Conformal fractional derivative
• Complete discrimination system for polynomial method
• Dynamic properties
• Soliton