### 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 language | English (US) |
---|---|

Pages (from-to) | 4131-4136 |

Number of pages | 6 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 53 |

Issue number | 4 SUPPL. B |

State | Published - Apr 1996 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*53*(4 SUPPL. B), 4131-4136.

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 53, no. 4 SUPPL. B, pp. 4131-4136.

}

TY - JOUR

T1 - Perturbation theories of a discrete, integrable nonlinear Schrödinger equation

AU - Cai, David

AU - Bishop, A. R.

AU - Grønbech-Jensen, Niels

PY - 1996/4

Y1 - 1996/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000856829&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000856829&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000856829

VL - 53

SP - 4131

EP - 4136

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4 SUPPL. B

ER -