Abstract: The author derived the Backlund transformation and a soliton solution of one-dimensional nonlinear transmission line equation by using the homogeneous balance method.Theoretical analysis to the stability of this solution was done.The result indicates that the soliton solution is conditional stability at the meaning of Lyapunov linear stability.It shows that stable soliton can be existed in nonlinear transmission line.Based on the extended thought of the homogeneous balance method,another soliton solution and a solitary wave solution of the nonlinear transmission line equation were obtained.

Key words: nonlinear transmission line equation, homogeneous balance method, soliton solution