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Symmetries of the continuous and discrete KricheverNovikov equation
 Symmetry, Integrability and Geometry: Methods and Applications, vol.7, Article Number: 097 DOI: 10.3842/SIGMA.2011.097
, 2011
"... ar ..."
Symmetry, Integrability and Geometry: Methods and Applications Symmetries of the Continuous and Discrete Krichever–Novikov Equation ⋆
"... Abstract. A symmetry classification is performed for a class of differentialdifference equations depending on 9 parameters. A 6parameter subclass of these equations is an integrable discretization of the Krichever–Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1 ≤ n ..."
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Abstract. A symmetry classification is performed for a class of differentialdifference equations depending on 9 parameters. A 6parameter subclass of these equations is an integrable discretization of the Krichever–Novikov equation. The dimension n of the Lie point symmetry algebra satisfies 1 ≤ n
On Miura Transformations and VolterraType Equations Associated with the Adler–Bobenko–Suris Equations
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2008
"... We construct Miura transformations mapping the scalar spectral problems of the integrable lattice equations belonging to the Adler–Bobenko–Suris (ABS) list into the discrete Schrödinger spectral problem associated with Volterratype equations. We show that the ABS equations correspond to Bäcklund ..."
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Cited by 15 (8 self)
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transformations for some particular cases of the discrete Krichever–Novikov equation found by Yamilov (YdKN equation). This enables us to construct new generalized symmetries for the ABS equations. The same can be said about the generalizations of the ABS equations introduced by Tongas, Tsoubelis and Xenitidis
Bäcklund transformation for the KricheverNovikov Equation
 Intl. Math. Res. Notices
, 1998
"... (u 2 xx − r(u)) + cux, r (5) = 0 (1) appeared (up to change u = p(ũ), ˙p 2 = r(p)) in [1] for the first time in connection with study of finitegap solutions of the KadomtsevPetviashvili equation. The distinctive feature of the equation (1) is that, accordingly to [2], no differential substitution ..."
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Cited by 32 (2 self)
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(u 2 xx − r(u)) + cux, r (5) = 0 (1) appeared (up to change u = p(ũ), ˙p 2 = r(p)) in [1] for the first time in connection with study of finitegap solutions of the KadomtsevPetviashvili equation. The distinctive feature of the equation (1) is that, accordingly to [2], no differential
Lax Pair for the Adler (lattice KricheverNovikov) system
, 2001
"... In the paper [V. Adler, IMRN 1 (1998) 1–4] a lattice version of the KricheverNovikov equation was constructed. We present in this note its Lax pair and discuss its elliptic form. ..."
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Cited by 93 (8 self)
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In the paper [V. Adler, IMRN 1 (1998) 1–4] a lattice version of the KricheverNovikov equation was constructed. We present in this note its Lax pair and discuss its elliptic form.
The KnizhnikZamolodchikov equations for positive genus, and KricheverNovikov
"... Abstract. We give a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus with marked points. Globality means here that we use KricheverNovikov algebras of gauge and conformal symmetries (i.e. algebras of global symmetries) instead of loop and Virasoro algebras ..."
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Cited by 12 (9 self)
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Abstract. We give a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus with marked points. Globality means here that we use KricheverNovikov algebras of gauge and conformal symmetries (i.e. algebras of global symmetries) instead of loop and Virasoro
The WessZuminoWittenNovikov theory, KnizhnikZamolodchikov equations, and KricheverNovikov algebras, I
, 1998
"... Elements of a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus g are given. Sheaves of representations of affine KricheverNovikov algebras over a dense open subset of the moduli space of Riemann surfaces (respectively of smooth, projective complex curves) ..."
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Cited by 26 (14 self)
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Elements of a global operator approach to the WZWN theory for compact Riemann surfaces of arbitrary genus g are given. Sheaves of representations of affine KricheverNovikov algebras over a dense open subset of the moduli space of Riemann surfaces (respectively of smooth, projective complex curves
Trivalent graphs and solitons I.Krichever ∗ S.P.Novikov †
, 2000
"... It is shown that a real selfadoint operator of order 4 on the trivalent tree Γ3 has (L,A,B)triple deformations that preserve one energy level. Laplace type discrete symmetries of such operators are constructed. ..."
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It is shown that a real selfadoint operator of order 4 on the trivalent tree Γ3 has (L,A,B)triple deformations that preserve one energy level. Laplace type discrete symmetries of such operators are constructed.
HIGHER GENUS AFFINE LIE ALGEBRAS OF KRICHEVERNOVIKOV TYPE
 TALK PRESENTED AT THE INTERNATIONAL CONFERENCE ON DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS, AND APPLICATIONS, MUNICH, JULY 2005
, 2005
"... Classical affine Lie algebras appear e.g. as symmetries of infinite dimensional integrablesystems and are related to certain differentialequations. They are central extensions of current algebras associated to finitedimensional Lie algebras g. In geometric terms these current algebras might be desc ..."
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Cited by 4 (3 self)
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simple, abelian,...) a complete classification of (almost) graded central extensions is given. In particular, for g simple there exists a unique nontrivial (almost)graded extension class. The considered algebras are related to difference equations, special functions and play a role in Conformal Field Theory.
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