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Another Look On Recursion Operators
"... . Recursion operators of partial differential equations are identified with Backlund autotransformations of linearized diffieties. Relations to the classical concept and its recent Guthrie's generalization are discussed. Traditionally, a recursion operator of a PDE is a linear operator L acting on ..."
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Cited by 8 (5 self)
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. Recursion operators of partial differential equations are identified with Backlund autotransformations of linearized diffieties. Relations to the classical concept and its recent Guthrie's generalization are discussed. Traditionally, a recursion operator of a PDE is a linear operator L acting on symmetries: if f is a symmetry then so is Lf . This provides a convenient way to generate infinite families of symmetries (Olver [13]). Standard reference is [14]. The presence of a recursion operator has been soon recognized as one of the attributes of the complete integrability. An exact and rich theory has been developed within the class of evolution equations (see Fokas [2] and references therein). Recursion operators are, as a rule, nonlocal and so may turn out to be the symmetries they generate (giving a powerful source of nonlocal symmetries [10, 5]). A remarkable problem of inverting a recursion operator motivated Guthrie [3] to a generalization, with consequences for generation of n...
Homological Perturbation Theory And Computability Of Hochschild And Cyclic Homologies Of Cdgas
, 1997
"... . We establish an algorithm computing the homology of commutative dierential graded algebras (briey, CDGAs). The main tool in this approach is given by the Homological Perturbation Theory particularized for the algebra category (see [21]). Taking into account these results, we develop and rene some ..."
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Cited by 3 (1 self)
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. We establish an algorithm computing the homology of commutative dierential graded algebras (briey, CDGAs). The main tool in this approach is given by the Homological Perturbation Theory particularized for the algebra category (see [21]). Taking into account these results, we develop and rene some methods already known about the computation of the Hochschild and cyclic homologies of CDGAs. In the last section of the paper, we analyze the plocal homology of the iterated bar construction of a CDGA (p prime). 1. Introduction. The description of eÆcient algorithms of homological computation might be considered as a very important question in Homological Algebra, in order to use those processes mainly in the resolution of problems on algebraic topology; but this subject also inuence directly on the development of non so closedareas as Cohomological Physics (in this sense, we nd useful references in [12], [24], [25]) and Secondary Calculus ([14], [27], [28]). Working in the context ...
A Supersymmetry Approach To Poisson Structures Over Differential Equations
, 1995
"... . An exposition of Poisson structures theory over nonlinear partial differential equations is given. The approach is based on consideration of d h invariant Hamiltonian formalism in the superalgebra (E 1 ), d h being the horizontal differential. Relations between supersymmetriesand Poisson s ..."
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. An exposition of Poisson structures theory over nonlinear partial differential equations is given. The approach is based on consideration of d h invariant Hamiltonian formalism in the superalgebra (E 1 ), d h being the horizontal differential. Relations between supersymmetriesand Poisson structures are established. A local description of Poisson structures for the two cases is given: E 1 = J 1 (ß) and E being a system of evolution equations. 1. Basic algebraic structures related to nonlinear partial differential equations. When dealing with socalled integrable systems, one always meets with the following concepts:  symmetries,  conservation laws,  Hamiltonian maps (Poisson structures),  recursion operators. In fact, all these concepts can be defined 1 for any nonlinear partial differential equation and only the problem of existence depend on a particular type of the equation at hand. Moreover, the basic constructions are of a purely algebraic (cohomological, to be...
FOR SYMMETRIES OF DIFFERENTIAL EQUATIONS POSSESSING RECURSION OPERATORS
, 2001
"... Lie algebra structures for symmetries of differential equations possessing recursion operators I. S. Krasil’shchik ..."
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Lie algebra structures for symmetries of differential equations possessing recursion operators I. S. Krasil’shchik
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, 2001
"... On the horizontal gauge cohomology and nonremovability of the spectral parameter by ..."
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On the horizontal gauge cohomology and nonremovability of the spectral parameter by
Deformation and Recursion for the N = 2 α = 1 Supersymmetric KdVhierarchy
, 2002
"... Abstract. A detailed description is given for the construction of the deformation of the N = 2 supersymmetric α = 1 KdVequation, leading to the recursion operator for symmetries and the zeroth Hamiltonian structure; the solution to a longstanding problem. 1. ..."
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Abstract. A detailed description is given for the construction of the deformation of the N = 2 supersymmetric α = 1 KdVequation, leading to the recursion operator for symmetries and the zeroth Hamiltonian structure; the solution to a longstanding problem. 1.
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, 2002
"... nlin.SI/0201061 BiHamiltonian structure of the N=2 supersymmetric α = 1 KdV hierarchy ..."
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nlin.SI/0201061 BiHamiltonian structure of the N=2 supersymmetric α = 1 KdV hierarchy