Browsing by Author "Tu, MH"

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A note on integrability in matrix models
(1996-10-01)
Tu, MH
;
Shaw, JC
;
Yen, HC
;
應用數學系
;
Department of Applied Mathematics
Based on the bilinear relation approach, we show that the hermitian one-matrix model at finite N can be embedded into 1d Toda chain and (modified) KP hierarchy respectively with the same Wronskian-type tau function. We also point out that which hierarchy to take depends on the choice of the wave function for constructing the bilinear relation.
A note on integrability in matrix models
(1996-10-01)
Tu, MH
;
Shaw, JC
;
Yen, HC
;
應用數學系
;
Department of Applied Mathematics
Based on the bilinear relation approach, we show that the hermitian one-matrix model at finite N can be embedded into 1d Toda chain and (modified) KP hierarchy respectively with the same Wronskian-type tau function. We also point out that which hierarchy to take depends on the choice of the wave function for constructing the bilinear relation.
A note on the gauge equivalence between the Manin-Radul and Laberge-Mathieu super KdV hierarchies
(1998-05-22)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
The gauge equivalence between the Manin-Kadul and Labarge-Mathieu super KdV hierarchies is revisited. Apart from the Inami-Kanno transformation, we show that there is another gauge transformation which also possesses the cancnical 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.
Binary Darboux-Backlund transformations for the Manin-Radul super KdV hierarchy
(1998-09-01)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
We construct the supersymmetric extensions of the Darboux-Backlund transformations (DBTs) for the Manin-Radul super Korteweg-de Vries (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. (C) 1998 American Institute of Physics.
Canonical gauge equivalences of the sAKNS and sTB hierarchies
(1998-07-31)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
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.
Canonical Miura maps between the modified KP and KP hierarchies
(1997-07-07)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
We investigate the Hamiltonian nature of two Miura maps between the modified KP and KP hierarchies. We show that they are canonical, in the sense that the bi-Hamiltonian structure of the modified KP hierarchy is mapped to the bi-Hamiltonian structure of the KP hierarchy.
Canonical Miura maps between the modified KP and KP hierarchies
(1997-07-07)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
We investigate the Hamiltonian nature of two Miura maps between the modified KP and KP hierarchies. We show that they are canonical, in the sense that the bi-Hamiltonian structure of the modified KP hierarchy is mapped to the bi-Hamiltonian structure of the KP hierarchy.
Hamiltonian structures of generalized Manin-Radul super-KdV and constrained super KP hierarchies
(1999-06-01)
Tu, MH
;
Shaw, JC
;
應用數學系
;
Department of Applied Mathematics
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. (C) 1999 American Institute of Physics. [S0022-2488(99)02206-9].
Matrix formulation of Hamiltonian structures of constrained KP hierarchy
(1998-07-01)
Huang, WJ
;
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
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 multiconstraint 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. (C) 1998 American Institute of Physics. [S0022-2488(98)01207-9].
Miura and auto-Backlund transformations for the cKP and cmKP hierarchies
(1997-11-01)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
We construct the Miura and auto-Backlund transformations for the cKP and cmKP hierarchies. Both the eigenfunctions and the adjoint eigenfunctions of the hierarchies are used to trigger the transformations. The canonical properties of the constructed Miura and auto-Backlund transformations are also investigated. (C) 1997 American Institute of Physics.
Nonlocal extended conformal algebras associated with multiconstraint KP hierarchy and their free field realizations
(1998-06-30)
Shaw, JC
;
Tu, MH
;
應用數學系
;
物理研究所
;
Department of Applied Mathematics
We study the conformal properties of the multiconstraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extensions 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 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 held realizations of its associated nonlocal algebras.
On the Miura and Backlund transformations associated with the supersymmetric Gelfand-Dickey bracket
(1998-04-20)
Shaw, JC
;
Tu, MH
;
應用數學系
;
物理研究所
;
Department of Applied Mathematics
The supersymmetric version of the Miura and Backlund transformations associated with the supersymmetric Gelfand-Dickey bracket are investigated from the point of view of the Kupershmidt-Wilson theorem.
Solving the constrained KP hierarchy by gauge transformations
(1997-08-01)
Chau, LL
;
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
We solve the constrained Kadomtsev-Petviashvili (cKP) hierarchy by using the gauge transformation technique. We show that there are two kinds of gauge transformations which preserve the form of the Lax operator of the cKP hierarchy. One of them is differential type and the other is integral type. Through two such gauge transformations we obtain not only the Wronskian-type tau-functions for the cKP hierarchy, but also the binary-type tau-functions which have not been obtained before. (C) 1997 American Institute of Physics.
The constrained modified KP hierarchy and the generalized Miura transformations
(1997-11-07)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
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.
The hidden algebraic structure of the Kaup-Broer hierarchy
(1998-05-08)
Shaw, JC
;
Tu, MH
;
應用數學系
;
Department of Applied Mathematics
In this paper, we investigate the conformal algebra associated with the coupled Kaup-Broer hierarchy which is obtained from the coupled AKNS hierarchy by gauge transformation. We find that the algebraic structure hidden behind the coupled Kaup-Broer hierarchy can be revealed after mapping the Lax operator of the coupled Kaup-Broer hierarchy to a Yajima-Oikawa-type Lax operator. Furthermore, we show that the second Hamiltonian structure of the coupled Kaup-Broer hierarchy can be simplified by factorizing the Lax operator in multiplicative form and thus obtain the free-field realization of the associated algebras.