Constrained KP models as integrable matrix hierarchies
- Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607-7059 (United States)
- Instituto de Fisica Teorica-UNESP, Rua Pamplona 145, 01405-900 Sao Paulo (Brazil)
We formulate the constrained KP hierarchy (denoted by cKP {sub K+1,M}) as an affine [cflx sl](M+K+1) matrix integrable hierarchy generalizing the Drinfeld{endash}Sokolov hierarchy. Using an algebraic approach, including the graded structure of the generalized Drinfeld{endash}Sokolov hierarchy, we are able to find several new universal results valid for the cKP hierarchy. In particular, our method yields a closed expression for the second bracket obtained through Dirac reduction of any untwisted affine Kac{endash}Moody current algebra. An explicit example is given for the case [cflx sl](M+K+1), for which a closed expression for the general recursion operator is also obtained. We show how isospectral flows are characterized and grouped according to the semisimple {ital non-regular} element E of sl(M+K+1) and the content of the center of the kernel of E. {copyright} {ital 1997 American Institute of Physics.}
- DOE Contract Number:
- FG02-84ER40173
- OSTI ID:
- 513448
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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