Diverse soliton solutions to the nonlinear partial differential equations related to electrical transmission line

Abstract This paper introduces novel traveling wave solutions for the (1+1)-dimensional nonlinear telegraph equation (NLTE) and the (2+1)-dimensional nonlinear electrical transmission line equation (NETLE). These equations are pivotal in the transmission and propagation of electrical signals, with applications in telegraph lines, digital image processing, telecommunications, and network engineering. We applied the improved tanh technique combined with the Riccati equation to derive new solutions, showcasing various solitary wave patterns through 3D surface and 2D contour plots. These results provide more comprehensive solutions than previous studies and offer practical applications in communication systems utilizing solitons for data transmission. The proposed method demonstrates an efficient calculation process, aiding researchers in analyzing nonlinear partial differential equations in applied mathematics, physics, and engineering