Computing with solitons: A review and prospectus

We review work on computing with solitons, from the discovery of solitons in cellular automata, to an abstract model for particle computation (particle machines), to information transfer in collisions of (continuum) optical solitons, to state transformations in collisions of Manakov (vector) solitons. We conclude by discussing open problems and the prospects for practical applications using optical solitons in photorefractive crystals and other materials.