Hirota difference equation: IST, Darboux transformation and solitons
  Direct and inverse problems for the Hirota difference equation are considered. Jost solutions and scattering data are introduced and their properties are presented. Darboux transformation in a special case is shown to give evolution with respect to discrete time and a recursion procedure for consequent construction of the Jost solution at arbitrary time, if the initial value is given. Some properties of the soliton solutions are discussed. 
Andrei Pogrebkov
nlin.SI math-ph math.MP