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In this article, we apply the generalized projective Riccati equations method with the aid of symbolic computation to construct new exact traveling wave solutions with parameters for two nonlinear PDEs describing nonlinear transmission lines (NLTL). The first equation describes the model of governing wave propagation in the NLTL as nonlinear low-pass electrical lines. The second equation describes pulse narrowing nonlinear transmission lines. The obtained solutions include, kink and anti-kink solitons, bell (bright) and anti-bell (dark) solitary wave solutions, hyperbolic solutions and trigonometric solutions. Based on Kirchhoff’s current law and Kirchhoff’s voltage law, the given nonlinear PDEs have been derived and can be reduced to nonlinear ordinary differential equations (ODEs) using a simple transformation. The given method in this article is straightforward and concise, and it can also be applied to other nonlinear PDEs in mathematical physics.

The Generalized Projective Riccati Equations Method and its Applications to Nonlinear PDEs Describing Nonlinear Transmission Lines