Memories of Hirota’s method: application to the reduced Maxwell–Bloch system in the early 1970s

Abstract

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.