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 journalArticlepeer-review

6 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 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).

Original languageEnglish
Pages (from-to)631-646
Number of pages16
JournalCommunications in Mathematical Physics
Volume108
Issue number4
DOIs
Publication statusPublished - 1 Dec 1987
Externally publishedYes

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