Dynamics of solitary pulses in the nonlinear low-pass electrical transmission lines through the auxiliary equation method

摘要

Exact traveling soliton solutions for the nonlinear LC transmission line are investigated. Based on Kirchhoff$`$s laws, we derive in the continuum limit and in suitable scaled coordinates, an equation governing slowly modulated wave propagating through the line. Through the auxiliary equation method, we successfully derive various exact traveling wave solutions for such a media. This method is straightforward and concise, and it can also be applied to other nonlinear evolution equations. The obtained solutions include, kink and anti-kink solitons, bell (bright) and anti-bell (dark) solitary waves solutions, periodic, singular and exponential solutions. This method is general as it leads us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines.