Hierarchy of (2 + 1)-dimensional nonlinear Schrödinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras

S. Kakei; T. Ikeda; K. Takasaki

doi:10.1007/s00023-002-8638-1

Hierarchy of (2 + 1)-dimensional nonlinear Schrödinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras

S. Kakei^*, T. Ikeda, K. Takasaki

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

The hierarchy structure associated with a (2 + 1)-dimensional Nonlinear Schrödinger equation is discussed as an extension of the theory of the KP hierarchy. Several methods to construct special solutions are given. The relation between the hierarchy and a representation of toroidal Lie algebras are established by using the language of free fermions. A relation to the self-dual Yang-Mills equation is also discussed.

Original language	English
Pages (from-to)	817-845
Number of pages	29
Journal	Annales Henri Poincare
Volume	3
Issue number	5
DOIs	https://doi.org/10.1007/s00023-002-8638-1
Publication status	Published - 2002
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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10.1007/s00023-002-8638-1

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title = "Hierarchy of (2 + 1)-dimensional nonlinear Schr{\"o}dinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras",

abstract = "The hierarchy structure associated with a (2 + 1)-dimensional Nonlinear Schr{\"o}dinger equation is discussed as an extension of the theory of the KP hierarchy. Several methods to construct special solutions are given. The relation between the hierarchy and a representation of toroidal Lie algebras are established by using the language of free fermions. A relation to the self-dual Yang-Mills equation is also discussed.",

author = "S. Kakei and T. Ikeda and K. Takasaki",

note = "Funding Information: The authors would like to thank Dr. Yasuhiro Ohta, Dr. Yoshihisa Saito, Dr. Nari-masa Sasa for their interests and discussions. The first author is partially supported by Waseda University Grant for Special Research Project 2000A-155, and the Grant-in-Aid for Scientific Research (No. 12740115) from the Ministry of Education, Culture, Sports, Science and Technology.",

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doi = "10.1007/s00023-002-8638-1",

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T1 - Hierarchy of (2 + 1)-dimensional nonlinear Schrödinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras

AU - Kakei, S.

AU - Ikeda, T.

AU - Takasaki, K.

N1 - Funding Information: The authors would like to thank Dr. Yasuhiro Ohta, Dr. Yoshihisa Saito, Dr. Nari-masa Sasa for their interests and discussions. The first author is partially supported by Waseda University Grant for Special Research Project 2000A-155, and the Grant-in-Aid for Scientific Research (No. 12740115) from the Ministry of Education, Culture, Sports, Science and Technology.

PY - 2002

Y1 - 2002

N2 - The hierarchy structure associated with a (2 + 1)-dimensional Nonlinear Schrödinger equation is discussed as an extension of the theory of the KP hierarchy. Several methods to construct special solutions are given. The relation between the hierarchy and a representation of toroidal Lie algebras are established by using the language of free fermions. A relation to the self-dual Yang-Mills equation is also discussed.

AB - The hierarchy structure associated with a (2 + 1)-dimensional Nonlinear Schrödinger equation is discussed as an extension of the theory of the KP hierarchy. Several methods to construct special solutions are given. The relation between the hierarchy and a representation of toroidal Lie algebras are established by using the language of free fermions. A relation to the self-dual Yang-Mills equation is also discussed.

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SN - 1424-0637

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JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 5

ER -

Hierarchy of (2 + 1)-dimensional nonlinear Schrödinger equation, self-dual Yang-Mills equation, and toroidal Lie algebras

Abstract

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