Linearization of the Relativistic and Discrete-Time Toda-Lattices for Particular Boundary-Conditions

In a previous study we considered solutions to the Kac-Van Moerbeke and semi-infinite Toda, discrete modified KdV and nonlinear Schrodinger equations. Using the AKNS approach, solutions of these equations were related to continued-fraction solutions of certain Riccati equations. A method for linearizing the Kac-Van Moerbeke lattice was rederived and extended to all the above lattices. Our approach demonstrated the crucial role played by the boundary condition at the finite end. This study is extended here to the relativistic and discrete-time Toda lattices which have been introduced recently.