Integrable nonlinear PDEs on the half-line

For many years, the most important open problem associated with nonlinear integrable evolution equations was the solution of initial-boundary as opposed to initial value problems. A novel approach for the analysis of this problem was introduced by one of the authors. The linear limit of this approach gave rise to a completely new method for solving linear evolution PDEs. Later, it was realised that this method has much wider applicability and it is now referred to in Wikipedia as the Fokas method. Here, we review the implementation of this method to integrable nonlinear PDEs on the half-line.