Exotical solitons for an intrinsic fractional circuit using the sine-cosine method

Abstract

This work focuses on seeking soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission network obtained through the simplest sine-cosine method. The studied model is governed by a fractional nonlinear partial differential-difference equation in (2 + 1) spatio-temporal dimensions, and the method used to get exact solutions is simple, concise and well-known. We achieve for the model studied here that, the sought solutions specifically by means of the sine-cosine method are functions of all the capacitor's nonlinearities (quadratic and cubic) if and only if, we use the fourth-order spatial dispersion (FOSD)during the continuous media approximation. In contrast, in the absence of the FOSD term, the solutions only exist if, either the quadratic or the cubic nonlinearity is considered separately. In addition, the obtained solutions shapes are exotical, unexpected and novel. These findings (singular bright solitary waves, pulse, U-shaped and M-shaped waves trains) get many applications; for instance, codifying data in the allowed or forbidden band for the signal's transmission in the waveguides.