Construction of exotical soliton-like for a fractional nonlinear electrical circuit equation using differential-difference Jacobi elliptic functions sub-equation method
Emmanuel Fendzi-Donfack, Dipankar Kumar, E. Tala-Tebue, Laurent Nana, Jean Pierre Nguenang, A. Kenfack-Jiotsa
Abstract
The deal of this paper is to use the differential-difference Jacobi elliptic functions sub-equation method for constructing exact solutions of nonlinear electrical circuit including intrinsic fractional-order in the sense of Riemann–Liouville derivatives. According to the algorithm of a unified symbolic computation, we attain several solitons solutions as solitary waves train, singular kink-type soliton, doubly periodic solitons, grey and anti-grey soliton-like. These findings are emerged and constructed by means of the three Jacobi elliptic functions. These types of functions provide hyperbolic, trigonometric, exotic and doubly periodic fractional exact solutions which have not yet been reported in the studied model. For this studied model, The new solutions obtained are exotic soliton-like that have not been observed yet. And they provide new propagative’s modes through the cn, dn, sn Jacobi elliptic functions for the fractional nonlinear electrical pass band circuit. Therefore, further investigations on differential-difference Jacobi elliptic functions sub-equation method should help researchers to discover more soliton solutions for other nonlinear discrete systems.