Construction of new traveling and solitary wave solutions of a nonlinear PDE characterizing the nonlinear low-pass electrical transmission lines

In this study, we intend to analyze the traveling and several other solitary wave solutions in the nonlinear low-pass electrical transmission line model using the new mapping method, the new extended auxiliary equation method, and the extended Kudryashov method. A type of traveling and solitary wave solutions emerge, consisting of hyperbolic function, trigonometric, rational, periodic, and doubly periodic solutions that reflect kink, anti-kink wave solitons, bright-dark optical solitons, singular solitons, and other traveling waves. The three integration techniques applied are efficient, effective, and versatile for the creation of new bright, dark, singular, and non-singular periodic and solitary wave propagation solutions in nonlinear low-pass electrical transmission lines. To see the extant physical significance of the considered equation, we present some 2D and 3D figures for some solutions. We compare the obtained results with those obtained in the literature. We investigate and demonstrate the stability of the soliton solutions. (paper)