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Hamiltonian structure of . . .
, 1993
"... The level spacing distributions in the Gaussian Unitary Ensemble, both in the “bulk of the spectrum,” sin π(x−y) given by the Fredholm determinant of the operator with the sine kernel and on the “edge of π(x−y) the spectrum, ” given by the Airy kernel Ai(x)Ai ′ (y)−Ai(y)Ai ′ (x) (x−y), are determine ..."
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−y), are determined by compatible systems of nonautonomous Hamiltonian equations. These may be viewed as special cases of isomonodromic deformation equations for first order 2×2 matrix differential operators with regular singularities at finite points and irregular ones of Riemann index 1 or 2 at ∞. Their Hamiltonian
Hierarchy as well as Their Hamiltonian Structure
"... Based on zero curvature equations from semidirect sums of Lie algebras, we construct triintegrable couplings of the GiachettiJohnson (GJ) hierarchy of soliton equations and establish Hamiltonian structures of the resulting triintegrable couplings by the variational identity. ..."
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Based on zero curvature equations from semidirect sums of Lie algebras, we construct triintegrable couplings of the GiachettiJohnson (GJ) hierarchy of soliton equations and establish Hamiltonian structures of the resulting triintegrable couplings by the variational identity.
On the Hamiltonian structure of Ermakov systems
 J. Phys. A: Math. Gen
, 1996
"... A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to quadratures. The Hamiltonian structure is explored to find exact ..."
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Cited by 3 (1 self)
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A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to quadratures. The Hamiltonian structure is explored to find
Hamiltonian structure of PI hierarchy
, 2006
"... The string equation of type (2,2g+1) may be thought of as a higher order analogue of the first Painlevé equation that correspond to the case of g = 1. For g> 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called the ..."
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Cited by 2 (0 self)
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the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can
Hamiltonian Structure of PI Hierarchy
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2007
"... The string equation of type (2, 2g + 1) may be thought of as a higher order analogue of the first Painlevé equation that corresponds to the case of g = 1. For g> 1, this equation is accompanied with a finite set of commuting isomonodromic deformations, and they altogether form a hierarchy called ..."
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called the PI hierarchy. This hierarchy gives an isomonodromic analogue of the well known Mumford system. The Hamiltonian structure of the Lax equations can be formulated by the same Poisson structure as the Mumford system. A set of Darboux coordinates, which have been used for the Mumford system, can
Hamiltonian structures for PaisUhlenbeck oscillator
, 2005
"... The hamiltonian structures for quartic oscillator are considered. All structures admitting quadratic hamiltonians are classified. supported by the ̷Lód´z University grant No. 690. ..."
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Cited by 3 (0 self)
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The hamiltonian structures for quartic oscillator are considered. All structures admitting quadratic hamiltonians are classified. supported by the ̷Lód´z University grant No. 690.
Hamiltonian structure of thermodynamics with gauge
, 2001
"... Denoting by q i (i = 1,..., n) the set of extensive variables which characterize the state of a thermodynamic system, we write the associated intensive variables γ i, the partial derivatives of the entropy S = S ( q 1,..., q n) ≡ q0, in the form γ i = −pi/p0 where p0 behaves as a gauge factor. When ..."
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Cited by 4 (0 self)
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. When regarded as independent, the variables q i, pi (i = 0,..., n) define a space T having a canonical symplectic structure where they appear as conjugate. A thermodynamic system is represented by a n + 1dimensional gaugeinvariant Lagrangean submanifold M of T. Any thermodynamic process, even
Hamiltonian structures for general PDEs
, 812
"... Summary. We sketch out a new geometric framework to construct Hamiltonian operators for generic, nonevolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, CamassaHolm equation, and Kupershmidt’s deformation of a biHamiltonian system. 1 ..."
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Cited by 1 (1 self)
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Summary. We sketch out a new geometric framework to construct Hamiltonian operators for generic, nonevolutionary partial differential equations. Examples on how the formalism works are provided for the KdV equation, CamassaHolm equation, and Kupershmidt’s deformation of a biHamiltonian system. 1
Results 1  10
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3,616