Bullough also contributed to nonlinear mathematical physics, including Bose–Einstein condensation in magnetic traps.

[2] On leaving school at 16, Bullough obtained a scholarship to Emmanuel College, Cambridge but had to do National Service in the RAF in 1948 and 1949.

Three days before his demobilisation he had an accident, putting a rawl plug into a wall, as a piece of steel from a chisel flew into his left eye.

He obtained a BA in Natural Sciences at Cambridge, specialising in Theoretical Physics for Part II.

By 1973 his research group in UMIST had found solutions to the sine-Gordon and the self-induced transparency (SIT) equations for their multi-soliton solutions and gone on to both introduce, and to solve the initial value problem for, the system they called the ‘Reduced Maxwell-Bloch (RMB) Equations’.

In 1999 he gave the specially invited 'Special Foundation Lecture' at the Fourteenth UK National Quantum Electronics & Photonics Conference (QEP14)[4] held at the University of Manchester.