New Classical and Quantum Integrable Systems Related to the MKdV Integrable Hierarchy

Ruguang Zhou; Wen-Xiu Ma

doi:10.1143/JPSJ.67.4045

New Classical and Quantum Integrable Systems Related to the MKdV Integrable Hierarchy

Ruguang Zhou
, Wen-Xiu Ma

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

15 Citations (Scopus)

Abstract

A new finite-dimensional classical integrable system and a new quantum integrable system are generated from a spectral problem for the MKdV hierarchy through the nonlinearization technique of Lax systems. Our classical integrable system is an example of Gaudin magnet with boundary and relates to the finite band solutions of the MKdV hierarchy. Its Lax representation and r-matrix is given, and its separation of variables is performed. Based on a direct link between r-matrix formulas for classical systems and quantum problems, a quantum integrable system with separated variables is presented.
© 1998 The Physical Society of Japan

Original language	English
Pages (from-to)	4045-4050
Journal	Journal of the Physical Society of Japan
Volume	67
Issue number	12
DOIs	https://doi.org/10.1143/JPSJ.67.4045
Publication status	Published - Dec 1998
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Integrable system
Nonlinearization of Lax system
r-matrix
The MKdV hierarchy

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abstract = "A new finite-dimensional classical integrable system and a new quantum integrable system are generated from a spectral problem for the MKdV hierarchy through the nonlinearization technique of Lax systems. Our classical integrable system is an example of Gaudin magnet with boundary and relates to the finite band solutions of the MKdV hierarchy. Its Lax representation and r-matrix is given, and its separation of variables is performed. Based on a direct link between r-matrix formulas for classical systems and quantum problems, a quantum integrable system with separated variables is presented. {\textcopyright} 1998 The Physical Society of Japan",

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AU - Ma, Wen-Xiu

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N2 - A new finite-dimensional classical integrable system and a new quantum integrable system are generated from a spectral problem for the MKdV hierarchy through the nonlinearization technique of Lax systems. Our classical integrable system is an example of Gaudin magnet with boundary and relates to the finite band solutions of the MKdV hierarchy. Its Lax representation and r-matrix is given, and its separation of variables is performed. Based on a direct link between r-matrix formulas for classical systems and quantum problems, a quantum integrable system with separated variables is presented. © 1998 The Physical Society of Japan

AB - A new finite-dimensional classical integrable system and a new quantum integrable system are generated from a spectral problem for the MKdV hierarchy through the nonlinearization technique of Lax systems. Our classical integrable system is an example of Gaudin magnet with boundary and relates to the finite band solutions of the MKdV hierarchy. Its Lax representation and r-matrix is given, and its separation of variables is performed. Based on a direct link between r-matrix formulas for classical systems and quantum problems, a quantum integrable system with separated variables is presented. © 1998 The Physical Society of Japan

KW - Integrable system

KW - Nonlinearization of Lax system

KW - r-matrix

KW - The MKdV hierarchy

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DO - 10.1143/JPSJ.67.4045

M3 - RGC 21 - Publication in refereed journal

SN - 0031-9015

VL - 67

SP - 4045

EP - 4050

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

IS - 12

ER -

New Classical and Quantum Integrable Systems Related to the MKdV Integrable Hierarchy

Abstract

Bibliographical note

Research Keywords

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