Multiple soliton solutions of the nonlinear partial differential equations describing the wave propagation in nonlinear low–pass electrical transmission lines

Abstract

This paper focuses on investigating soliton and other solutions using three integration schemes to integrate a nonlinear partial differential equation describing the wave propagation in nonlinear low–pass electrical transmission lines. By applying the Kirchhoff’s laws and complex transformation, the nonlinear low–pass electrical transmission lines are converted into an equation wave propagation in nonlinear ODE low–pass electrical transmission lines. Later on, mentioned integration schemes viz modified Kudryashov method, sine–Gordon equation expansion method and extended sinh–Gordon equation expansion method are used to carry out new hyperbolic and trigonometric solutions which shows the consistency via computerized symbolic computation package maple. Various types of solitary wave solutions are derived including kink, anti-kink, dark, bright, dark-bright, singular, combined singular, and periodic singular wave soliton solutions. The corresponding three integration schemes are robust and effective for acquiring the new dark, bright, dark–bright, singular or combined singular and optical soliton solutions of the wave propagation in nonlinear low–pass electrical transmission lines. To show the real physical significance of the studied equation, some three dimensional (3D) and two dimensional (2D) figures of obtained solutions are plotted with the use of the Matlab software under the proper choice of arbitrary parameters. Moreover, all derived solutions were verified back into its corresponding equation with the aid of maple program.