Search Results - "Igonin, Sergei"

Simplifications of Lax pairs for differential–difference equations by gauge transformations and (doubly) modified integrable equations by Igonin, Sergei

“…Matrix differential–difference Lax pairs play an essential role in the theory of integrable nonlinear differential–difference equations. We present sufficient…”
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On Lie algebras responsible for integrability of (1+1)-dimensional scalar evolution PDEs by Igonin, Sergei, Manno, Gianni

“…Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In [13], for any (1+1)-dimensional scalar evolution…”
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Lie algebras responsible for zero-curvature representations of scalar evolution equations by Igonin, Sergei, Manno, Gianni

“…Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In particular, Lax pairs for (1+1)-dimensional PDEs can be…”
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On construction of symmetries and recursion operators from zero-curvature representations and the Darboux–Egoroff system by Igonin, Sergei, Marvan, Michal

“…The Darboux–Egoroff system of PDEs with any number n≥3 of independent variables plays an essential role in the problems of describing n-dimensional flat…”
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Simplifications of Lax pairs for differential-difference equations by gauge transformations and (doubly) modified integrable equations by Igonin, Sergei

“…Partial Differential Equations in Applied Mathematics 11 (2024), 100821 Matrix differential-difference Lax pairs play an essential role in the theory of…”
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On Lax representations under the gauge equivalence relation and Miura-type transformations for lattice equations by Igonin, Sergei

“…We study matrix Lax representations (MLRs) for differential-difference (lattice) equations. For a given equation, two MLRs are said to be gauge equivalent if…”
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Set-theoretical solutions to the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability by Igonin, Sergei

“…Theoretical and Mathematical Physics 212 (2022), 1116--1124 This paper is devoted to tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov…”
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On matrix Lax representations and constructions of Miura-type transformations for differential-difference equations by Chistov, Evgeny, Igonin, Sergei

“…This paper is part of a research project on relations between differential-difference matrix Lax representations (MLRs) with the action of gauge…”
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Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation by Igonin, Sergei, Konstantinou-Rizos, Sotiris

“…We present several algebraic and differential-geometric constructions of tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron…”
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On Lie algebras responsible for integrability of (1+1)-dimensional scalar evolution PDEs by Igonin, Sergei, Manno, Gianni

“…Journal of Geometry and Physics 150 (2020), 103596 Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In…”
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Lie algebras responsible for zero-curvature representations of scalar evolution equations by Igonin, Sergei, Manno, Gianni

“…Journal of Geometry and Physics 138 (2019), 297-316 Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In…”
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On Lie algebras responsible for zero-curvature representations and Backlund transformations of (1+1)-dimensional scalar evolution PDEs by Igonin, Sergei, Manno, Gianni

“…Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In particular, Lax pairs for $(1+1)$-dimensional PDEs can be…”
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On Lie algebras responsible for zero-curvature representations of multicomponent (1+1)-dimensional evolution PDEs by Igonin, Sergei, Manno, Gianni

“…Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable $(1+1)$-dimensional PDEs. According to the preprint…”
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Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations by Berkeley, George, Igonin, Sergei

“…J. Phys. A: Math. Theor. 49 (2016), 275201 Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential…”
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On construction of symmetries and recursion operators from zero-curvature representations and the Darboux-Egoroff system by Igonin, Sergei, Marvan, Michal

“…J. Geom. Phys. 85 (2014), 106--123 The Darboux-Egoroff system of PDEs with any number $n\ge 3$ of independent variables plays an essential role in the problems…”
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Notes on homogeneous vector bundles over complex flag manifolds by Igonin, Sergei

“…V.A.Malyshev and A.M.Vershik (eds.), Asymptotic Combinatorics with Application to Mathematical Physics, 245-254. Kluwer, 2002 Let P be a parabolic subgroup of…”
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Conservation laws for multidimensional systems and related linear algebra problems by Igonin, Sergei

“…J. Phys. A: Math. Gen. 35 (2002) 10619-10628 We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order…”
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Conservation laws of generalized higher Burgers and linear evolution equations by Igonin, Sergei

“…By the Cole-Hopf transformation, with any linear evolution equation in 1+1 dimensions a generalized Burgers equation is associated. We describe local…”
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Prolongation structure of the Krichever-Novikov equation by Igonin, Sergei, Martini, Ruud

“…J. Phys. A: Math. Gen. 35 (2002) 9801-9810 We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, u_x, u_{xx}, u_{xxx}…”
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On one-parametric families of Backlund transformations by Igonin, Sergei, Krasil'shchik, Joseph

“…In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of Backlund transformations of special type…”
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