Modified constrained KP hierarchy and bi-Hamiltonian structures

In this paper, we review various properties of the supersymmetric Two-Boson (sTB) system. We discuss the equation and its nonstandard Lax representation. We construct the local conserved charges as well as the Hamiltonian structures of the system, and show how this system leads to various other known supersymmetric integrable models under appropriate field redefinition. We discuss the sTB and the supersymmetric nonlinear Schrödinger (sNLS) equations as constrained, nonstandard supersymmetric Kadomtsev-Petviashvili (sKP) systems and note that the nonstandard sKP systems naturally unify all the KP and mKP flows while leading to a new integrable supersymmetrization of the KP equation. We construct the nonlocal conserved charges associated with the sTB system and show that the algebra of charges corresponds to a graded, cubic algebra. Also, we note that the sTB system has a hidden supersymmetry making it an N=2 extended supersymmetric system.

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The hamiltonian structures of the KP hierarchy

Physics Letters B ◽

10.1016/0370-2693(91)91285-4 ◽

1991 ◽

Vol 271 (1-2) ◽

pp. 109-115 ◽

Cited By ~ 18

Author(s):

Ashok Das ◽

Wen-Jui Huang ◽

Sudhakar Panda

Keyword(s):

Kp Hierarchy ◽

Hamiltonian Structures

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A NOTE ON THE KP HIERARCHY

Modern Physics Letters A ◽

10.1142/s0217732392001531 ◽

1992 ◽

Vol 07 (20) ◽

pp. 1825-1833 ◽

Cited By ~ 2

Author(s):

DIDIER A. DEPIREUX

Keyword(s):

Hamiltonian Structure ◽

Conformal Algebra ◽

Kp Hierarchy ◽

Hamiltonian Structures ◽

Boson Representation

Given the two boson representation of the conformal algebra Ŵ∞, the second Hamiltonian structure of the KP hierarchy, I construct a bi-Hamiltonian hierarchy for the two associated currents. The KP hierarchy appears as a composite of this new and simpler system. The bi-Hamiltonian structure of the new hierarchy gives naturally all the Hamiltonian structures of the KP system.

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NONLOCAL EXTENDED CONFORMAL ALGEBRAS ASSOCIATED WITH MULTICONSTRAINT KP HIERARCHY AND THEIR FREE FIELD REALIZATIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x98001384 ◽

1998 ◽

Vol 13 (16) ◽

pp. 2723-2737

Author(s):

JIIN-CHANG SHAW ◽

MING-HSIEN TU

Keyword(s):

Hamiltonian Structure ◽

Free Field ◽

Kp Hierarchy ◽

Hamiltonian Structures ◽

Integer Spin ◽

Half Integer ◽

Conformal Algebras ◽

Spin Fields ◽

Lax Operator

We study the conformal properties of the multiconstraint KP hierarchy and its non-standard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extensions of Wn algebra by some integer or half-integer spin fields depending on the order of the Lax operators. In particular, we show that the complicated second Hamiltonian structure of the nonstandard multiconstraint KP hierarchy can be simplified by factorizing its Lax operator to multiplication form. We then diagonalize this simplified Poisson matrix and obtain the free field realizations of its associated nonlocal algebras.

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