Kac-Moody symmetry of generalized non-linear Schrödinger equations

A. D.W.B. Crumey

doi:10.1007/BF01217759

Kac-Moody symmetry of generalized non-linear Schrödinger equations

A. D.W.B. Crumey^*

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

The classical non-linear Schrödinger equation associated with a symmetric Lie algebra g{script}=k⊕m is known to possess a class of conserved quantities which from a realization of the algebra k⊗ℂ [λ]. The construction is now extended to provide a realization of the Kac-Moody algebra k⊗ℂ[λ, λ^-1] (with central extension). One can then define auxiliary quantities to obtain the full algebra g{script}⊗ℂ[λ, λ^-1]. This leads to the formal linearization of the system.

Original language	English
Pages (from-to)	167-179
Number of pages	13
Journal	Communications in Mathematical Physics
Volume	111
Issue number	2
DOIs	https://doi.org/10.1007/BF01217759
Publication status	Published - Jun 1987
Externally published	Yes

Keywords

Neural Network
Statistical Physic
Complex System
Nonlinear Dynamics
Formal Linearization

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10.1007/BF01217759

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abstract = "The classical non-linear Schr{\"o}dinger equation associated with a symmetric Lie algebra g\{script\}=k⊕m is known to possess a class of conserved quantities which from a realization of the algebra k⊗ℂ [λ]. The construction is now extended to provide a realization of the Kac-Moody algebra k⊗ℂ[λ, λ-1] (with central extension). One can then define auxiliary quantities to obtain the full algebra g\{script\}⊗ℂ[λ, λ-1]. This leads to the formal linearization of the system.",

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author = "Crumey, \{A. D.W.B.\}",

year = "1987",

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N2 - The classical non-linear Schrödinger equation associated with a symmetric Lie algebra g{script}=k⊕m is known to possess a class of conserved quantities which from a realization of the algebra k⊗ℂ [λ]. The construction is now extended to provide a realization of the Kac-Moody algebra k⊗ℂ[λ, λ-1] (with central extension). One can then define auxiliary quantities to obtain the full algebra g{script}⊗ℂ[λ, λ-1]. This leads to the formal linearization of the system.

AB - The classical non-linear Schrödinger equation associated with a symmetric Lie algebra g{script}=k⊕m is known to possess a class of conserved quantities which from a realization of the algebra k⊗ℂ [λ]. The construction is now extended to provide a realization of the Kac-Moody algebra k⊗ℂ[λ, λ-1] (with central extension). One can then define auxiliary quantities to obtain the full algebra g{script}⊗ℂ[λ, λ-1]. This leads to the formal linearization of the system.

KW - Neural Network

KW - Statistical Physic

KW - Complex System

KW - Nonlinear Dynamics

KW - Formal Linearization

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DO - 10.1007/BF01217759

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SP - 167

EP - 179

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -

Kac-Moody symmetry of generalized non-linear Schrödinger equations

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Keywords

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