Constraints of the Kadomtsev–Petviashvili hierarchy

Cheng, Yi

doi:10.1063/1.529875

Cited by 220 publications

(202 citation statements)

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“…The modified flows are defined on the phase space Θ by pulling back the Hamiltonians H Q j in (8) by means of the map µ. For reasons explained in [9] (see also [1,2]), if s = 0 the factor…”

Section: Modifications Of Extended Gelfand-dickey Hierarchiesmentioning

confidence: 99%

“…There have been several papers over the last few years devoted to systems of the above type [1][2][3][4][5][6][7][8]. It was shown in [9] how hierarchies with a Lax operator of the form in (1) can be obtained by the Drinfeld-Sokolov (DS) reduction method.…”

Section: Introductionmentioning

confidence: 99%

“…It was shown in [9] how hierarchies with a Lax operator of the form in (1) can be obtained by the Drinfeld-Sokolov (DS) reduction method. Specifically, with the partition n = pr + s = p times r + · · · + r + s times 1 + · · · + 1 (2) is associated [11] a graded Heisenberg subalgebra of the loop algebra gl n ⊗ C I [λ, λ −1 ], and a generalised KdV hierarchy having the Lax operator in (1) results from application of the DS reduction procedure [10] (see also [12,13,14]) with respect to a grade-one element from this Heisenberg subalgebra, if r > 1. In the r = 1 special case the DS reduction becomes trivial, but interesting results remain valid.…”

Section: Introductionmentioning

confidence: 99%

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Extended matrix Gelfand - Dickey hierarchies: reduction to classical Lie algebras

Fehér

Marshall

1997

J. Phys. A: Math. Gen.

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The Drinfeld-Sokolov reduction method has been used to associate with gl n extensions of the matrix r-KdV system. Reductions of these systems to the fixed point sets of involutive Poisson maps, implementing reduction of gl n to classical Lie algebras of type B, C, D, are here presented. Modifications corresponding, in the first place to factorisation of the Lax operator, and then to Wakimoto realisations of the current algebra components of the factorisation, are also described.

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Section: Modifications Of Extended Gelfand-dickey Hierarchiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended matrix Gelfand - Dickey hierarchies: reduction to classical Lie algebras

Fehér

Marshall

1997

J. Phys. A: Math. Gen.

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“…Either (2+1)-dimensional soliton equations [1], [2] or (1+1) -dimensio -nal soliton equations [3], [4] can be decomposed into two compatible finite-dimensional integrable systems. It is known that a crucial idea in carrying out symmetry constraints is the nonlinearization of Lax pairs for soliton hierarchies.…”

Section: Introductionmentioning

confidence: 99%

Bargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

Tao¹

2013

IJAPM

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Abstract-An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Guo hierarchy. Under the obtained symmetry constraint, the n-th flow of the super Guo hierarchy is decomposed into two super finite -dimensional integrable Hamiltonian systems, which defined over the super symmetry manifold R 4N|2N with the corresponding dynamical variables x and t n . The integrals of motion required for Liouville integrability are explicitly given.Index Terms-Symmetry constraint, binary nonlinearization, super guo hierarchy, super finitee-dimensional integrable hamiltonian systems. I. INTRODUCTIONFor almost twenty years, much attention has been paid to the construction of finite-dimensional integrable systems from soliton equations by using symmetry constraints. Either [19]. In this paper, we would like to consider the binary nonlinearization of the super Guo hierarchy. This paper is organized as follows. In the next section, we will recall the super Guo soliton hierarchy and its super Hamiltonian structure. Then in Section III, we compute a Bargmann symmetry constraint for the potential of the super Guo hierarchy. In Section IV, we apply the binary nonlinearization method to super Guo hierarchy, and then obtain super finite-dimensional integrable Hamiltonian hierarchy on the super symmetry manifold ℝ 4 |2 , whose integrals of motion are explicitly given. II. THE SUPER GUO HIERARCHYwhere is a spectral parameter, q and r are even variables, and and are odd variables(see [20] ). Taking If we setthen (2) Si-Xing TaoBargmann Symmetry Constraint and Binary Nonlinearization of Super Guo Hierarchy

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“…The new type of reduced Kadomtsev-Petviashvili (KP) hierarchy, called the constrained KP hierarchy, was introduced in [KSS91,KS92], where it was observed that the YO hierarchy can be obtained as a constrained KP hierarchy (and this was used in [Che92] to find its bi-Poisson structure). A more general s-vector constrained KP hierarchy was introduced in [SS93], where it was shown that the multi-component YO hierarchy, studied in [Ma81], can be obtained by this construction.…”

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confidence: 99%