For the optical transmission of data across a cable, one can use two (or more) coupled fibre cables. Experiments have shown that if a certain type of signal is put at one end of the cable, it will go to the other end of this cable and hardly anything happens in the other cable. However, if one puts other types of signals on the cable, the signal will switch to the other cable. This gives a convenient way of sending data consisting of zeros and ones.
It is an open question how this process exactly works and why certain signals do switch and others don't. A mathematical model for the process is given by a set of partial differential equations called the ``coupled nonlinear Schrodinger equations''. The experimentally observed signals behave like so-called solitons (very sharply peaked waves). The soliton solutions of the mathematical model can be described by an ordinary differential equation, which conserves energy and has some extra symmetries.
In this project we will aim for a better understanding of the experimentally observed process of soliton switching in a nonlinear directional fibre coupler. In order to achieve this aim, we will investigate the family of soliton-like solutions in the model equation for pulse propagation in an ideal nonlinear directional fibre coupler. Issues such as existence, stability, bifurcations and invariant manifolds will be investigated. We will then aim to find which soliton solutions are relevant for nonlinear directional fibre couplers with some perturbations such as damping and forcing.