Nonlinear Schrödinger model with boundary, integrability and scattering matrix based on the degenerate affine hecke algebra

Yasushi Komori; Kazuhiro Hikami

doi:10.1142/S0217751X97002887

Nonlinear Schrödinger model with boundary, integrability and scattering matrix based on the degenerate affine hecke algebra

Yasushi Komori, Kazuhiro Hikami

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

The δ-function interacting many-body systems (nonlinear Schrödinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang-Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrödinger model are investigated.

Original language	English
Pages (from-to)	5397-5410
Number of pages	14
Journal	International Journal of Modern Physics A
Volume	12
Issue number	30
DOIs	https://doi.org/10.1142/S0217751X97002887
Publication status	Published - 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

Atomic and Molecular Physics, and Optics
Nuclear and High Energy Physics
Astronomy and Astrophysics

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10.1142/S0217751X97002887

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title = "Nonlinear Schr{\"o}dinger model with boundary, integrability and scattering matrix based on the degenerate affine hecke algebra",

abstract = "The δ-function interacting many-body systems (nonlinear Schr{\"o}dinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang-Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schr{\"o}dinger model are investigated.",

author = "Yasushi Komori and Kazuhiro Hikami",

note = "Funding Information: The authors would like to thank Miki Wadati for kind interest in this work. They also thank M. Shiroishi and S. Murakami for stimulating discussions. This work is supported in part by the Grant-in-Aid from the Ministry of Education, Science, Sports and Culture, of Japan.",

year = "1997",

doi = "10.1142/S0217751X97002887",

language = "English",

volume = "12",

pages = "5397--5410",

journal = "International Journal of Modern Physics A",

issn = "0217-751X",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "30",

}

TY - JOUR

T1 - Nonlinear Schrödinger model with boundary, integrability and scattering matrix based on the degenerate affine hecke algebra

AU - Komori, Yasushi

AU - Hikami, Kazuhiro

N1 - Funding Information: The authors would like to thank Miki Wadati for kind interest in this work. They also thank M. Shiroishi and S. Murakami for stimulating discussions. This work is supported in part by the Grant-in-Aid from the Ministry of Education, Science, Sports and Culture, of Japan.

PY - 1997

Y1 - 1997

N2 - The δ-function interacting many-body systems (nonlinear Schrödinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang-Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrödinger model are investigated.

AB - The δ-function interacting many-body systems (nonlinear Schrödinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang-Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrödinger model are investigated.

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U2 - 10.1142/S0217751X97002887

DO - 10.1142/S0217751X97002887

M3 - Article

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SN - 0217-751X

VL - 12

SP - 5397

EP - 5410

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

IS - 30

ER -

Nonlinear Schrödinger model with boundary, integrability and scattering matrix based on the degenerate affine hecke algebra

Abstract

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