PERTURBATION THEORIES OF A DISCRETE, INTEGRABLE NONLINEAR SCHRODINGER-EQUATION

We rederive the discrete inverse-scattering transform (IST) perturbati on results for the time evolution of the parameters of a discrete nonl inear Schrodinger soliton from certain mathematical identities that ca n be viewed as conserved quantities in the discrete, integrable nonlin ear Schrodinger equation in (1+1) dimension. This method significantly simplifies the derivation of the IST perturbation results. We also pr esent a specific example for which the adiabatic IST perturbation resu lts and the collective coordinate method results exactly coincide. Thi s is achieved by establishing a correct Lagrangian formalism for solit on parameters via transforming dynamical variables that obey a deforme d Poisson structure to ones that possess a canonical Poisson structure .