The Direct Method in Soliton Theory

Hirota invented his bilinear or direct method in the early 1970s as a way of constructing soliton solutions without dealing with the cumbersome inverse scattering transform. His invention has since come to the Kyoto School and became connected with affine Lie algebras, but here Hirota explains the more modern version of the method, in which solutions are expressed in the form of determinants and pfaffians. Hirota covers elementary properties of linear and nonlinear waves and eave expressions, the properties of determinants and pfaffians, and gives examples of soliton equations, finishing with a discussion of Bäcklund transforms.