Invariant solutions and bifurcation analysis of the nonlinear transmission line model

In this paper, the nonlinear transmission line model with power law nonlinearity and constant capacitance voltage relationship is studied using Lie symmetry analysis. Corresponding to infinitesimals obtained, commutation relations, abelian non-abelian subalgebras are obtained. Also, adjoint table, a one-dimensional optimal system of subalgebra presented. Based on system, corresponding reductions Moreover, variety new similarity solutions in form trigonometric functions, hyperbolic one reduction, by bifurcation analysis dynamical stable unstable regions determined, which show existence soliton from dynamics point view. Some obtained represented graphically observations also discussed.