Local and non-local conserved quantities for generalized non-linear Schrödinger equations

A. D.W.B. Crumey

doi:10.1007/BF01214421

Local and non-local conserved quantities for generalized non-linear Schrödinger equations

A. D.W.B. Crumey^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

It is shown how to construct infinitely many conserved quantities for the classical non-linear Schrödinger equation associated with an arbitrary Hermitian symmetric space G/K. These quantities are non-local in general, but include a series of local quantities as a special case. Their Poisson bracket algebra is studied, and is found to be a realization of the "half" Kac-Moody algebra k_R ⊗ ℂ [λ], consisting of polynomials in positive powers of a complex parameter λ which have coefficients in the compact real form of k (the Lie algebra of K).

Original language	English
Pages (from-to)	631-646
Number of pages	16
Journal	Communications in Mathematical Physics
Volume	108
Issue number	4
DOIs	https://doi.org/10.1007/BF01214421
Publication status	Published - 1 Dec 1987
Externally published	Yes

Access to Document

10.1007/BF01214421

Cite this

@article{631fb4dba0e642b7947820eb5812c6c8,

title = "Local and non-local conserved quantities for generalized non-linear Schr{\"o}dinger equations",

abstract = "It is shown how to construct infinitely many conserved quantities for the classical non-linear Schr{\"o}dinger equation associated with an arbitrary Hermitian symmetric space G/K. These quantities are non-local in general, but include a series of local quantities as a special case. Their Poisson bracket algebra is studied, and is found to be a realization of the {"}half{"} Kac-Moody algebra kR ⊗ ℂ [λ], consisting of polynomials in positive powers of a complex parameter λ which have coefficients in the compact real form of k (the Lie algebra of K).",

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

year = "1987",

month = dec,

day = "1",

doi = "10.1007/BF01214421",

language = "English",

volume = "108",

pages = "631--646",

journal = "Communications in Mathematical Physics",

issn = "0010-3616",

publisher = "Springer",

number = "4",

}

TY - JOUR

T1 - Local and non-local conserved quantities for generalized non-linear Schrödinger equations

AU - Crumey, A. D.W.B.

PY - 1987/12/1

Y1 - 1987/12/1

N2 - It is shown how to construct infinitely many conserved quantities for the classical non-linear Schrödinger equation associated with an arbitrary Hermitian symmetric space G/K. These quantities are non-local in general, but include a series of local quantities as a special case. Their Poisson bracket algebra is studied, and is found to be a realization of the "half" Kac-Moody algebra kR ⊗ ℂ [λ], consisting of polynomials in positive powers of a complex parameter λ which have coefficients in the compact real form of k (the Lie algebra of K).

AB - It is shown how to construct infinitely many conserved quantities for the classical non-linear Schrödinger equation associated with an arbitrary Hermitian symmetric space G/K. These quantities are non-local in general, but include a series of local quantities as a special case. Their Poisson bracket algebra is studied, and is found to be a realization of the "half" Kac-Moody algebra kR ⊗ ℂ [λ], consisting of polynomials in positive powers of a complex parameter λ which have coefficients in the compact real form of k (the Lie algebra of K).

U2 - 10.1007/BF01214421

DO - 10.1007/BF01214421

M3 - Article

AN - SCOPUS:34250100257

SN - 0010-3616

VL - 108

SP - 631

EP - 646

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 4

ER -

Local and non-local conserved quantities for generalized non-linear Schrödinger equations

Abstract

Access to Document

Fingerprint

Cite this