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On Recursion Operators
"... We observe that application of a recursion operator of Burgers equation does not produce the expected symmetries. This is explained by the incorrect assumption that D−1x Dx = 1. We then proceed to give a method to compute the symmetries using the recursion operator as a first order approximation. ..."
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We observe that application of a recursion operator of Burgers equation does not produce the expected symmetries. This is explained by the incorrect assumption that D−1x Dx = 1. We then proceed to give a method to compute the symmetries using the recursion operator as a first order approximation.
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 actin ..."
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Cited by 14 (8 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
Integrable Systems and their Recursion Operators
, 2001
"... In this paper we discuss the structure of recursion operators. We show that recursion operators of evolution equations have a nonlocal part that is determined by symmetries and cosymmetries. This enables us to compute recursion operators more systematically. Under certain conditions (which hold for ..."
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Cited by 1 (1 self)
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In this paper we discuss the structure of recursion operators. We show that recursion operators of evolution equations have a nonlocal part that is determined by symmetries and cosymmetries. This enables us to compute recursion operators more systematically. Under certain conditions (which hold
On recursion operators for elliptic models
 Nonlinearity
"... Abstract. New quasilocal recursion and Hamiltonian operators for the KricheverNovikov and the LandauLifshitz equations are found. It is shown that the associative algebra of quasilocal recursion operators for these models is generated by a couple of operators related by an elliptic curve equation. ..."
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Cited by 3 (0 self)
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Abstract. New quasilocal recursion and Hamiltonian operators for the KricheverNovikov and the LandauLifshitz equations are found. It is shown that the associative algebra of quasilocal recursion operators for these models is generated by a couple of operators related by an elliptic curve equation
Recursion operator for the IGSG equation
, 2006
"... In this paper we find the inverse and direct recursion operator for the intrinsic generalized sineGordon equation in any number n> 2 of independent variables. Among the flows generated by the direct operator we identify a higherdimensional analogue of the pmKdV equation. Key words. Submanifolds ..."
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Cited by 3 (1 self)
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In this paper we find the inverse and direct recursion operator for the intrinsic generalized sineGordon equation in any number n> 2 of independent variables. Among the flows generated by the direct operator we identify a higherdimensional analogue of the pmKdV equation. Key words
TimeDependent Recursion Operators and Symmetries
, 2002
"... The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their recursion operators do not satisfy the symmetry equations. Ther ..."
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Cited by 1 (0 self)
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The recursion operators and symmetries of nonautonomous, (1 + 1) dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their recursion operators do not satisfy the symmetry equations
Process Algebra with Recursive Operations
"... ing from just the two atomic actions in I def = fthrow; tailg, FIR b 1 yields I ((throw tail) throw head) = head: First, observe I (throw tail) = . Then, using (4), it easily follows that I ((throw tail) throw head) = head: This expresses that head eventually comes up, and thus ex ..."
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Cited by 14 (5 self)
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), its introduction is nontrivial because at the same time it must be a unit for k as well. In the design of BPA, PA, ACP and related axiom systems, it has proved useful to study versions of the theory, both with and without ". Just for this reason the star operation with its (original) defining
THE GEOMETRY OF RECURSION OPERATORS
, 2007
"... ABSTRACT. We study the fields of endomorphisms intertwining pairs of symplectic structures. Using these endomorphisms we prove an analogue of Moser’s theorem for simultaneous isotopies of two families of symplectic forms. We also consider the geometric structures defined by pairs and triples of symp ..."
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Cited by 2 (0 self)
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ABSTRACT. We study the fields of endomorphisms intertwining pairs of symplectic structures. Using these endomorphisms we prove an analogue of Moser’s theorem for simultaneous isotopies of two families of symplectic forms. We also consider the geometric structures defined by pairs and triples of symplectic forms for which the squares of the intertwining endomorphisms are plus or minus the identity. For pairs of forms we recover the notions of symplectic pairs and of holomorphic symplectic structures. For triples we recover the notion of a hypersymplectic structure, and we also find three new structures that have not been considered before. One of these is the symplectic formulation of hyperKähler geometry, which turns out to be a strict generalization of the usual definition in terms of differential or Kähler geometry. 1.
Noncommutative Integrability and Recursion Operators
, 1999
"... Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant (1,1) tensor field. The construction of compatible symplectic ..."
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Cited by 2 (1 self)
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Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant (1,1) tensor field. The construction of compatible symplectic structures is also discussed.
Recursion operators and Frobenius manifolds
 SIGMA
, 2012
"... In this short note I wish to present some ideas of a recent comparative study of three different types of manifolds which are of interest in different areas of physics and mathematics. They are: 1) Fmanifolds; ..."
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Cited by 1 (0 self)
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In this short note I wish to present some ideas of a recent comparative study of three different types of manifolds which are of interest in different areas of physics and mathematics. They are: 1) Fmanifolds;
Results 1  10
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