Perturbation theories of a discrete, integrable nonlinear Schrödinger equation

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

Research output: Contribution to journalArticle

Abstract

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
Volume53
Issue number4 SUPPL. B
StatePublished - Apr 1996

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Integrable Equation
inverse scattering
Inverse Scattering Transform
Perturbation Theory
nonlinear equations
Nonlinear Equations
perturbation theory
perturbation
Poisson Structure
solitary waves
Perturbation
Solitons
Conserved Quantity
derivation
formalism
Simplify

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Perturbation theories of a discrete, integrable nonlinear Schrödinger equation. / Cai, David; Bishop, A. R.; Grønbech-Jensen, Niels.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 53, No. 4 SUPPL. B, 04.1996, p. 4131-4136.

Research output: Contribution to journalArticle

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