Perturbation theories of a discrete, integrable nonlinear Schr{umlt o}dinger equation
We rederive the discrete inverse-scattering transform (IST) perturbation results for the time evolution of the parameters of a discrete nonlinear Schr{umlt o}dinger soliton from certain mathematical identities that can be viewed as conserved quantities in the discrete, integrable nonlinear Schr{umlt o}dinger equation in (1+1) dimension. This method significantly simplifies the derivation of the IST perturbation results. We also present a specific example for which the adiabatic IST perturbation results and the collective coordinate method results exactly coincide. This is achieved by establishing a correct Lagrangian formalism for soliton parameters via transforming dynamical variables that obey a deformed Poisson structure to ones that possess a canonical Poisson structure. {copyright} {ital 1996 The American Physical Society.}
- OSTI ID:
- 283819
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 53; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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