Rapidly Decreasing Solution of the Initial Boundary-Value Problem for the Toda Lattice - Khanmamedov, A. Kh. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
Using the inverse scattering transform, we investigate an initial boundary-value problem with zero boundary condition for the Toda lattice. We prove the existence and uniqueness of a rapidly decreasing solution and determine a class of initial data that guarantees the existence of a rapidly decreasing solution.