Affine Lie algebraic origin of constrained KP hierarchies

Journal Article · Sat Jul 01 04:00:00 EDT 1995 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.530970· OSTI ID:69058

Aratyn, H ^[1]; Gomes, J F; Zimerman, A H ^[2]

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1. Department of Physics, University of Illinois at Chicago, 845 W. Taylor St., Chicago, Illinois 60607-7059 (United States)
2. Instituto de Fisica Teorica-UNESP, Rua Pamplona 145, 01405-900 Sao Paulo (Brazil)

An affine {ital sl}({ital n}+1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schroedinger @(s@Gs@Ns@LsS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Baecklund transformations and interpolate between@ s@Gs@Ns@LsS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

• DOE Contract Number: FG02-84ER40173
• OSTI ID: 69058
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 7 Vol. 36; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BAECKLUND TRANSFORMATION
BOSONS
FIELD THEORIES
LIE GROUPS
MATHEMATICAL OPERATORS
SCHROEDINGER EQUATION
WAVE EQUATIONS