Perturbation theories of a discrete, integrable nonlinear Schr{umlt o}dinger equation

Journal Article · Mon Apr 01 04:00:00 EST 1996 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.53.4131· OSTI ID:283819

Cai, D; Bishop, A R

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

Related Subjects

66 PHYSICS
INVERSE SCATTERING PROBLEM
LAGRANGIAN FUNCTION
NONLINEAR PROBLEMS
PERTURBATION THEORY
SCHROEDINGER EQUATION
SOLITONS
TIMING PROPERTIES