Optical and W-shaped bright solitons of the conformable derivative nonlinear differential equation

Abstract

In this paper, we construct diverse solitary wave solutions for the nonlinear differential equation governing wave propagation in the low-pass nonlinear electrical transmission lines with conformable derivatives. However, by employing the new extended direct algebraic method and the improved Sub-ODE equation, we recovered W-shape bright soliton, dark soliton, periodic solutions, rational solutions and Weierstrass elliptic function solutions. The obtained results are new in nonlinear electrical transmission lines field. In addition, the acquired solitons are depicted with the appropriate parameters values of the methods and the nonlinear electrical transmission lines. The shape of the W-bright and dark soliton solutions points out the effect of the derivative order. Finally, the results indicate that the two integrations methods are a most applicable and forceful integration tools for emphasizing the soliton solutions.