Nonlinear phenomena, optical and quantum solitons.

Research in the theory of solitons and its applications has undergone impressive development in recent years and has affected a broad range of fields, including theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups and discrete geometry among others. Robin K. Bullough (21 November 1929–30 August 2008) was a British mathematical physicist famous for his contributions to the theory of solitons. In particular, he is known for his role in the development of the theory of the optical soliton, a term coined by him, and now commonly used, for example, in the theory of propagation of electromagnetic pulses in optical fibres. Bullough is also known for deriving exact solutions to nonlinear equations describing these solitons and for associated work on integrable systems, infinite-dimensional Hamiltonian systems (both classical and quantum) and the statistical mechanics of these systems. His famous Grand Synthesis of Soliton Theory, a huge diagram containing a vast array of areas in mathematics and mathematical physics, with connections (solid lines when established; dotted when expected), portrays the state of the art for about 10 years ago of the theory, and at the same time one of its strengths, namely its interdisciplinary character. Indeed, the diagram shows remarkable connections between seemingly disparate subjects. The diagram is a legacy of Robin: it perpetually evolves as dotted connections become solid and as new subject areas with corresponding links are added so that the diagram becomes increasingly more complex. Bullough obtained his first academic position in the Mathematics Department at UMIST in Manchester in 1960, and was appointed chair of Mathematical Physics in 1973, where he remained until his retirement in 1995. He was an Emeritus Professor at UMIST until 2004 and, following the merger with the Victoria University, in the School of Mathematics at the University of Manchester. He was active in research until the day he died. This Theme Issue has been put together as a special tribute to Robin K. Bullough. The selection of research papers brings together recent developments and findings, written by people with links to Robin, as colleagues, as students, as research assistants, as academic collaborators or simply as admirers of Robin’s many research achievements.