The Direct Method in Soliton Theory

The bilinear or Hirota''s direct method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the complex calculations of the inverse scattering transform. This analysis is essentially concerned with the more modern version of the method. Still maintaining the original philosophy of using relatively simple mathematics the method has nevertheless been influenced by the work of the Kyoto school and will be essential for all working in soliton theory.