The project “Multi-dimensional, Multi-Soliton Patch Interactions“, led by Matt Turner and Dave Lloyd, has been funded by the EPSRC Small Grants Panel. The project ran from October 2024 to September 2025. The award was for £92K and provided 40% and 10% staff time respectively and travel money. The project aims to investigate the weak interaction of solitons in the complex-quintic Ginzburg-Landau equation in multiple space dimensions. The project will formulate a fast and efficient numerical scheme to investigate the interactions by using a global centre-manifold reduction technique to split the motion into slowly evolving ODEs, coupled to a fast-evolving PDE for the coupling effect. The form of a two-dimensional soliton is shown in the figure below.
