Growth and damping of solitons in a nonlinear transmission line with moving parameters

A nonlinear dispersive inhomogeneous transmission line in which solitons grow or reduce their amplitudes exponentially without emitting any oscillatory tails is derived. In the one-directional approximation, the wave equation shown here can be still rewritten, through an explicit transformation, to the well-known Korteweg-de Vries equation which has a multiple interacting soliton solution.