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247,957
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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operators. The biHamiltonian nature of these systems is shown by a systematic construction of two general Poisson brackets on the algebra of associated Laxoperators. Gauge transformations provide Miura links to modified equations. These systems are constrained flows of the modified KP hierarchy, for which
A Plethora of Integrable BiHamiltonian Equations
, 1996
"... This paper discusses several algorithmic ways of constructing integrable evolution equations based on the use of multiHamiltonian structures. The recognition that integrable soliton equations, such as the KortewegdeVries (KdV) and nonlinear Schrodinger (NLS) equations, can be constructed using a b ..."
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Cited by 17 (4 self)
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This paper discusses several algorithmic ways of constructing integrable evolution equations based on the use of multiHamiltonian structures. The recognition that integrable soliton equations, such as the KortewegdeVries (KdV) and nonlinear Schrodinger (NLS) equations, can be constructed using a
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
BiHamiltonian Formulations of the Bateman Equation
, 1995
"... We discuss a class of evolution equations equivalent to the simplest Universal Field Equation, the so–called Bateman equation, and show that all of them possess (at least) biHamiltonian structure. The first few conserved charges are calculated. 0 1 ..."
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Cited by 1 (1 self)
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We discuss a class of evolution equations equivalent to the simplest Universal Field Equation, the so–called Bateman equation, and show that all of them possess (at least) biHamiltonian structure. The first few conserved charges are calculated. 0 1
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
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
A biHamiltonian structure for the integrable, discrete nonlinear Schrödinger system
 Physica D
"... This paper shows that the AL (Ablowitz–Ladik) hierarchy of (integrable) equations can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect to both a standard, local Poisson operator J, and a new nonlocal, skew, almost Poisson operator K, on the appropriate ..."
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Cited by 5 (0 self)
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space; (b) can be recursively generated from a recursion operator R = KJ −1. In addition, the proof of these facts relies upon two new pivotal resolvent identities which suggest a general method for uncovering biHamiltonian structures for other families of discrete, integrable equations.
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1554 (85 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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. A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter
A survey of generalpurpose computation on graphics hardware
, 2007
"... The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware acompelling platform for computationally demanding tasks in awide variety of application domains. In this report, we describe, summarize, and analyze the l ..."
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Cited by 545 (18 self)
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the latest research in mapping generalpurpose computation to graphics hardware. We begin with the technical motivations that underlie generalpurpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim
Results 1  10
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247,957