THE 2D TODA LATTICE AND THE ABLOWITZ-LADIK HIERARCHY

A relation between the 2D Toda lattice (2DTL) and the Ablowitz-Ladik h ierarchy is established. This relation is used to reinvestigate the in verse scattering transform for the 2DTL. The 2DTL is an integrable sys tem in 2 + 1 dimensions that has been integrated previously by means o f the multi-dimensional inverse scattering method. In the present work it is shown to be solvable in the framework of the traditional, one-d imensional, inverse scattering method. A corresponding scheme, similar to the one developed for the discrete nonlinear Schrodinger equation, is elaborated. Using the method proposed, the Gelfand-Levitan-Marchen ko equation is derived together with the conservation laws and soliton solutions.