Memories of Hirota's method: application to the reduced Maxwell-Bloch system in the early 1970s.

@article{Caudrey2011MemoriesOH,
  title={Memories of Hirota's method: application to the reduced Maxwell-Bloch system in the early 1970s.},
  author={P. J. Caudrey},
  journal={Philosophical transactions. Series A, Mathematical, physical, and engineering sciences},
  year={2011},
  volume={369 1939},
  pages={1215-27}
}
Who remembers 'Hirota's method'? In the early days of solitons, although the Korteweg-de Vries equation had been solved by the 'inverse scattering method' most solutions to integrable non-linear equations were found by simpler more direct methods. Outstanding among these was a method due mainly to Hirota, which involved casting the equation into a 'bilinear form' and then applying intelligent guesswork. In this paper, I shall take a journey down memory lane, looking again at this method.