Nonlinear Schrödinger solitons in the forced Toda lattice (Q1096811)

I demonstrate that the pulsating oscillations observed by Hill and Knopoff in the forced Toda lattice may be interpreted as nonlinear Schrödinger solitons. This is accomplished by taking the small amplitude and the continuum limit of the forced Toda lattice equation. This limit is shown to be the stable form of the nonlinear Schrödinger equation. However, ``dark'' solitons can be expected to occur for this form since in this case the nonlinear Schrödinger field can be consider to approach a nonzero value at infinity. I then demonstrate that one can interpret these pulsating oscillations in terms of these dark nonlinear Schrödinger solitons.