Perturbation theories of a discrete, integrable nonlinear schrödinger equation

David Cai, A. R. Bishop, Niels Grønbech-Jensen

Research output: Contribution to journalArticlepeer-review


We rederive the discrete inverse-scattering transform (IST) perturbation results for the time evolution of the parameters of a discrete nonlinear Schrödinger soliton from certain mathematical identities that can be viewed as conserved quantities in the discrete, integrable nonlinear Schrödinger 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.

Original languageEnglish (US)
Pages (from-to)4131-4136
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number4
StatePublished - 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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