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Constrained KP Hierarchy and BiHamiltonian Structures
, 1993
"... The KadomtsevPetviashvili (KP) hierarchy is considered together with the evolutions of eigenfunctions and adjoint eigenfunctions. Constraining the KP flows in terms of squared eigenfunctions one obtains 1+1dimensional integrable equations with scattering problems given by pseudodifferential Lax o ..."
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again a general description of their biHamiltonian nature is given. The gauge transformations are shown to be Poisson maps relating the biHamiltonian structures of the constrained KP hierarchy and the modified KP hierarchy. The simplest realization of this scheme yields the AKNS hierarchy and its
BiHamiltonian structure of super KP hierarchy
"... We obtain the biHamiltonian structure of the super KP hierarchy based on the even super KP operator Λ = θ 2 + ∑ ∞ i=−2 Uiθ −i−1, as a supersymmetric extension of the ordinary KP biHamiltonian structure. It is expected to give rise to a universal super Walgebra incorporating all known extended sup ..."
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Cited by 4 (0 self)
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We obtain the biHamiltonian structure of the super KP hierarchy based on the even super KP operator Λ = θ 2 + ∑ ∞ i=−2 Uiθ −i−1, as a supersymmetric extension of the ordinary KP biHamiltonian structure. It is expected to give rise to a universal super Walgebra incorporating all known extended
Canonical forms for biHamiltonian systems
 In Integrable systems (Luminy
, 1991
"... BiHamiltonian systems were first defined in the fundamental paper of Magri, [5], which deduced the integrability of many soliton equations from the fact that they could be written in Hamiltonian form in two distinct ways. More recently, the classical completely integrable Hamiltonian systems of ordi ..."
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Cited by 1 (0 self)
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general completely integrable Hamiltonian system.) The connection between biHamiltonian structures and Rmatrices, [10], which provide solutions to the classical YangBaxter equation, has given additional impetus to their study. Magri’s Theorem demonstrates the existence of an infinite hierarchy
The BiHamiltonian Structure of the Perturbation Equations of the KdV
, 1996
"... The biHamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general biHamiltonian integrable hierarchy is proposed and a remark is given for a genera ..."
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Cited by 15 (8 self)
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The biHamiltonian structure is established for the perturbation equations of KdV hierarchy and thus the perturbation equations themselves provide also examples among typical soliton equations. Besides, a more general biHamiltonian integrable hierarchy is proposed and a remark is given for a
BiHamiltonian representation of Stäckel systems
, 904
"... It is shown that a linear separation relations are fundamental objects for integration by quadratures of Stäckel separable Liouville integrable systems (the socalled Stäckel systems). These relations are further employed for the classification of Stäckel systems. Moreover, we prove that any Stäckel ..."
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Stäckel separable Liouville integrable system can be lifted to a biHamiltonian system of Gel’fandZakharevich type. In conjunction with other known result this implies that the existence of biHamiltonian representation of Liouville integrable systems is a necessary condition for Stäckel separability. 1
BiHamiltonian representation of Stäckel systems
, 2009
"... It is shown that the separation relations are fundamental objects for integration by quadratures of separable Liouville integrable systems (the socalled Stäckel systems). These relations are further employed for the classification of separable systems. Moreover, we prove that any separable Liouvill ..."
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Liouville integrable system can be lifted to a biHamiltonian system of Gel’fandZakharevich type. In conjunction with other known result this implies that the existence of biHamiltonian representation of Liouville integrable systems is a necessary condition for separability.
BiHamiltonian reductions and Wnalgebras
 J. Geom. Phys. 26
, 1998
"... We discuss the geometry of the Marsden–Ratiu reduction theorem for a bihamiltonian manifold. We consider the case of the manifolds associated with the Gel’fand– Dickey theory, i.e., loop algebras over sln. We provide an explicit identification, tailored on the MR reduction, of the Adler–Gel’fand–Dic ..."
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Cited by 5 (3 self)
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We discuss the geometry of the Marsden–Ratiu reduction theorem for a bihamiltonian manifold. We consider the case of the manifolds associated with the Gel’fand– Dickey theory, i.e., loop algebras over sln. We provide an explicit identification, tailored on the MR reduction, of the Adler
ON THE BIHAMILTONIAN THEORY FOR THE HARRY DYM EQUATION
, 2001
"... Abstract. We describe how the Harry Dym equation fits into the the biHamiltonian formalism for the Kortewegde Vries equation and other soliton equations. This is achieved by means of a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev ..."
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Abstract. We describe how the Harry Dym equation fits into the the biHamiltonian formalism for the Kortewegde Vries equation and other soliton equations. This is achieved by means of a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue
Results 1  10
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17,142