Waves are ubiquitous, occuring throughout the natural world. Describing their propagation and interaction is of prime importance. My research in this area has focussed on the Korteweg-de Vries (KdV) equation, which describes waves of small amplitude on shallow water. The KdV equation has a travelling wave solution called a soliton, which is a single humped wave. This nonlinear equation has the very special property that the collision of two solitons leaves them unchanged in shape. Of interest is the solitons home page at Heriot-Watt University, which has movies of soliton interactions, historical information and links to many other sites devoted to this topic.
I have been working on solitary wave interaction and evolutions for higher-order extensions to integrable models such as the KdV, NLS and Hirota equations. Listed below are some recent papers of mine on this topic