The AKNS hierarchy revisited: A vertex operator approach and its lie-algebraic structure

Denis Blackmore; Anatoliy K. Prykarpatsky

doi:10.1142/S1402925112500015

The AKNS hierarchy revisited: A vertex operator approach and its lie-algebraic structure

Denis Blackmore, Anatoliy K. Prykarpatsky

Mathematical Sciences

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

3 Scopus citations

Abstract

A novel approach based upon vertex operator representation is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed.

Original language	English (US)
Article number	1250001
Journal	Journal of Nonlinear Mathematical Physics
Volume	19
Issue number	1
DOIs	https://doi.org/10.1142/S1402925112500015
State	Published - Mar 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

AKNS hierarchy
Lax integrability
Lie-algebraic approach
vertex operators

Access to Document

10.1142/S1402925112500015

Cite this

@article{9828a7af2eef4fa1bb43635b7705eb10,

title = "The AKNS hierarchy revisited: A vertex operator approach and its lie-algebraic structure",

abstract = "A novel approach based upon vertex operator representation is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed.",

keywords = "AKNS hierarchy, Lax integrability, Lie-algebraic approach, vertex operators",

author = "Denis Blackmore and Prykarpatsky, {Anatoliy K.}",

note = "Funding Information: D. Blackmore wishes to thank the National Science Foundation for support from NSF Grant CMMI — 1029809 and his coauthor for enlisting him in the efforts that produced this paper. Special thanks are due to the Scientific and Technology Research Council of Turkey (TUBITAK-2011) for partial support of the research of A. K. Prykarpatsky. A. K. Prykarpatsky cordially thanks Profs. M. V. Pavlov and V. H. Samoylenko for very useful discussions of the results obtained. The authors also wish to express their appreciation to the reviewers whose insightful comments helped to improve the paper.",

year = "2012",

month = mar,

doi = "10.1142/S1402925112500015",

language = "English (US)",

volume = "19",

journal = "Journal of Nonlinear Mathematical Physics",

issn = "1402-9251",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

T1 - The AKNS hierarchy revisited

T2 - A vertex operator approach and its lie-algebraic structure

AU - Blackmore, Denis

AU - Prykarpatsky, Anatoliy K.

N1 - Funding Information: D. Blackmore wishes to thank the National Science Foundation for support from NSF Grant CMMI — 1029809 and his coauthor for enlisting him in the efforts that produced this paper. Special thanks are due to the Scientific and Technology Research Council of Turkey (TUBITAK-2011) for partial support of the research of A. K. Prykarpatsky. A. K. Prykarpatsky cordially thanks Profs. M. V. Pavlov and V. H. Samoylenko for very useful discussions of the results obtained. The authors also wish to express their appreciation to the reviewers whose insightful comments helped to improve the paper.

PY - 2012/3

Y1 - 2012/3

N2 - A novel approach based upon vertex operator representation is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed.

AB - A novel approach based upon vertex operator representation is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed.

KW - AKNS hierarchy

KW - Lax integrability

KW - Lie-algebraic approach

KW - vertex operators

UR - http://www.scopus.com/inward/record.url?scp=84858830570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858830570&partnerID=8YFLogxK

U2 - 10.1142/S1402925112500015

DO - 10.1142/S1402925112500015

M3 - Article

AN - SCOPUS:84858830570

SN - 1402-9251

VL - 19

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

IS - 1

M1 - 1250001

ER -

The AKNS hierarchy revisited: A vertex operator approach and its lie-algebraic structure

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this