This thesis describes an investigation into various aspects of periodically amplified nonlinear systems, in which solitons play a central role. A new nonlinear oscillator is introduced. The Baseband Soliton Oscillator (BSO) is fashioned from a loop of nonlinear transmission line. The oscillator supports an endlessly circulating Korteweg-de Vries (KdV) soliton - and more generally, exhibits the periodic cnoidal and double cnoidal solutions. Frequency dependent losses are shown to be responsible for the stability of the BSO. The double cnoidal oscillation allows subtle aspects of soliton-soliton interaction to be identified. A novel nonlinear partial differential equation is derived to capture the dynamics of the BSO. Uniform and viscous losses are added to the KdV equation, while a periodic inhomogeneity models the amplification. The steady states of this equation are sought numerically and found to agree with the experimental results. A new technique based on the Method of Multiple Scales is advanced to derive average equations for periodically amplified systems described by either the lossy KdV or Nonlinear Schrodinger (NLS) equation. The method proceeds by explicitly considering the nonlinear and dispersive effects as perturbations between amplifiers. Although the concept of an average NLS equation is well known, the average KdV equation is novel. The result is verified numerically. Including the effects of frequency dependent losses in the average KdV description yields an accurate steady state analysis of the BSO. An envelope soliton analogue of the BSO is advanced. The Envelope Soliton Oscillator (ESO) endlessly circulates an envelope soliton. The device is a close electronic analogue of the Soliton Fibre Ring Laser, in that it includes an amplifier, bandpass filter, nonlinear transmission line and saturable absorber. It is shown that the saturable absorber promotes the formation of solitons in the ESO. Studies of the perturbed average KdV equation reveal the asymptotic widths of average KdV solitons can be found via a direct method. The steady state is found by equating the gain to the dissipation, assuming a constant pulse shape between amplifiers. It is shown that this analysis is also applicable to periodically amplified NLS systems, and thus to optical soliton communication links.