Video solitons in a dispersive transmission line with the nonlinear capacitance of a $p$–$n$ junction

Possible types of low-frequency electromagnetic solitary waves in a dispersive $LC$ transmission line with a quadratic or cubic capacitive nonlinearity are investigated. The fourth-order nonlinear wave equation with ohmic losses is derived from the differential-difference equations of the discrete line in the continuum approximation. For a zero-loss line, this equation can be reduced to the nonlinear equation for a transmission line, the double dispersion equation, the Boussinesq equations, the Korteweg–de Vries (KdV) equation, and the modified KdV equation. Solitary waves in a transmission line with dispersion and dissipation are considered.