HIROTA DIFFERENCE EQUATION: INVERSE SCATTERING TRANSFORM, 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. In a special case Darboux transformation is shown to enable description of the 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.