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Jiin-Chang Shaw

Publications and source records attributed to Jiin-Chang Shaw.

9 recordsLinked to original sources
arXiv1998

Hamiltonian Structures of Generalized Manin-Radul Super KdV and Constrained Super KP Hierarchies

A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami-Kanno super KdV hierarchy and constrained modified super KP hierarchy are investigated from the reduced supersymmetric Gelfand-Dickey brackets. By applying a gauge transformation on the Hamiltonian structures associated with these two nonstandard super Lax hierarchies, we obtain the Hamiltonian structures of generalized Manin-Radul super KdV and constrained super KP hierarchies. We also work out a few examples and compare them with the known results.

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arXiv1998

On Darboux-Bäcklund Transformations for the Q-Deformed Korteweg-de Vries Hierarchy

We study Darboux-Bäcklund transformations (DBTs) for the $q$-deformed Korteweg-de Vries hierarchy by using the $q$-deformed pseudodifferential operators. We identify the elementary DBTs which are triggered by the gauge operators constructed from the (adjoint) wave functions of the hierarchy. Iterating these elementary DBTs we obtain not only $q$-deformed Wronskian-type but also binary-type representations of the tau-function to the hierarchy.

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arXiv1998

Matrix Formulation of Hamiltonian Structures of Constrained KP Hierarchy

We give a matrix formulation of the Hamiltonian structures of constrained KP hierarchy. First, we derive from the matrix formulation the Hamiltonian structure of the one-constraint KP hierarchy, which was originally obtained by Oevel and Strampp. We then generalize the derivation to the multi-constraint case and show that the resulting bracket is actually the second Gelfand-Dickey bracket associated with the corresponding Lax operator. The matrix formulation of the Hamiltonian structure of the one-constraint KP hierarchy in the form introduced in the study of matrix model is also discussed

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arXiv1997

Canonical gauge equivalences of the sAKNS and sTB hierarchies

We study the gauge transformations between the supersymmetric AKNS (sAKNS) and supersymmetric two-boson (sTB) hierarchies. The Hamiltonian nature of these gauge transformations is investigated, which turns out to be canonical. We also obtain the Darboux-Backlund transformations for the sAKNS hierarchy from these gauge transformations.

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arXiv1997

A Note on the Gauge Equivalence between the Manin-Radul and Laberge-Mathieu Super KdV Hierarchies

The gauge equivalence between the Manin-Radul and Laberge-Mathieu super KdV hierarchies is revisited. Apart from the Inami-Kanno transformation, we show that there is another gauge transformation which also possess the canonical property. We explore the relationship of these two gauge transformations from the Kupershmidt-Wilson theorem viewpoint and, as a by-product, obtain the Darboux-Backlund transformation for the Manin-Radul super KdV hierarchy. The geometrical intepretation of these transformations is also briefly discussed.

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arXiv1997

Binary Darboux-Backlund Transformations for the Manin-Radul Super KdV Hierarchy

We construct the supersymmetric extensions of the Darboux-Backlund transformations (DBTs) for the Manin-Radul super KdV hierarchy using the super-pseudo-differential operators. The elementary DBTs are triggered by the gauge operators constructed from the wave functions and adjoint wave functions of the hierarchy. Iterating these elementary DBTs, we obtain not only Wronskian type but also binary type superdeterminant representations of the solutions.

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arXiv1997

Nonlocal extended conformal algebras associated with multi-constraint KP hierarchy and their free-field realizations

We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of $W_n$ 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 multi-constraint 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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arXiv1997

The constrained modified KP hierarchy and the generalized Miura transformations

In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.

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