Soliton computing in the Toda lattice: controllable delay and logic gates

Most people take the technological revolution from the past two centuries for granted and expect that this revolution will not slow down. In the recent century, a major presence in most people's lives has become electronic computers in one form or another. A new path for technology innovations needs to be set out if the revolution is to continue at the current pacing. One such promising path are optical computers using solitons as information carriers. Solitons have favourable properties and one under-explored soliton system for its computation capabilities is the Toda lattice, which has been used to model DNA and can be transformed into optical fibre models. By expanding the possible logic gate designs in this lattice, steps are made to bring us closer to realize a fully functional optical computer. In the one-dimensional Toda lattice, it is possible to create a delay in the solitons' travels that can be controlled. The lattice has been used to create logic gates for computation, however, the delay mechanism has not been incorporated in those designs so far. With this controllable delay, an OR and XOR gate can be designed. The delay for a travelling soliton is created by incorporating a lattice made of harmonic oscillators between two Toda lattices. The duration of the delay can be controlled by changing the time difference of two solitons scattering against the harmonic oscillators. If the duration is too short, there are only reflections, however, when the duration between the two soltions' scatterings is long enough, transmission is possible. Both presented logic gates apply the controllable delay mechanism. This thesis contains the following contributions, the first investigation of interaction of solitons in impurity, a new XOR and OR gate design, and code for simulating the Toda lattice and the mentioned contributions.