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Found 132 Documents (Results 1–100)

The finite-gap method and the periodic Cauchy problem for \((2+1)\)-dimensional anomalous waves for the focusing Davey-Stewartson 2 equation. (English. Russian original) Zbl 1522.35465

Russ. Math. Surv. 77, No. 6, 1029-1059 (2022); translation from Usp. Mat. Nauk 77, No. 6, 77-108 (2022).
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Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves. (English. Russian original) Zbl 1484.14072

Russ. Math. Surv. 76, No. 4, 587-652 (2021); translation from Usp. Mat. Nauk 76, No. 4, 37-104 (2021).
MSC:  14H70 14K25 37J35
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Conway topograph, \(\operatorname{PGL}_2(\mathbb{Z})\)-dynamics and two-valued groups. (English. Russian original) Zbl 1484.11153

Russ. Math. Surv. 74, No. 3, 387-430 (2019); translation from Usp. Mat. Nauk 74, No. 3, 17-62 (2019).
MSC:  11H55 20N20 37P99
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Liouville integrability of the reduction of the associativity equations on the set of stationary points of an integral in the case of three primary fields. (English. Russian original) Zbl 1439.37069

Russ. Math. Surv. 74, No. 2, 369-371 (2019); translation from Usp. Mat. Nauk 74, No. 2,191-192 (2019).
MSC:  37K10 37K20 37K30
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Polynomial graph invariants and linear hierarchies. (English. Russian original) Zbl 1439.37070

Russ. Math. Surv. 74, No. 2, 366-368 (2019); translation from Usp. Mat. Nauk 74, No. 2, 189-190 (2019).
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Trace formula for the magnetic Laplacian. (English. Russian original) Zbl 1433.58019

Russ. Math. Surv. 74, No. 2, 325-361 (2019); translation from Usp. Mat. Nauk 74, No. 2, 149-186 (2019).
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The finite-gap method and the periodic NLS Cauchy problem of anomalous waves for a finite number of unstable modes. (English. Russian original) Zbl 1454.35340

Russ. Math. Surv. 74, No. 2, 211-263 (2019); translation from Usp. Mat. Nauk 74, No. 2, 27-80 (2019).
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Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter. (English. Russian original) Zbl 1439.37062

Russ. Math. Surv. 74, No. 1, 141-173 (2019); translation from Usp. Mat. Nauk 74, No. 1, 149-184 (2019).
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Polynomial Hamiltonian integrable systems on symmetric powers of plane curves. (English. Russian original) Zbl 1419.14053

Russ. Math. Surv. 73, No. 6, 1122-1124 (2018); translation from Usp. Mat. Nauk 73, No. 6, 193-194 (2018).
MSC:  14H70 37J05 37J35
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Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin-Novikov type. (English. Russian original) Zbl 1393.37071

Russ. Math. Surv. 73, No. 1, 175-177 (2018); translation from Usp. Mat. Nauk 73, No. 1, 183-184 (2018).
MSC:  37K05 37K10 53D45 53B20
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Scientific heritage of L. D. Faddeev. Survey of papers. (English. Russian original) Zbl 1396.81008

Russ. Math. Surv. 72, No. 6, 977-1081 (2017); translation from Usp. Mat. Nauk 72, No. 6, xx (2017).
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On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator. (English. Russian original) Zbl 1330.81080

Russ. Math. Surv. 70, No. 2, 299-329 (2015); translation from Usp. Mat. Nauk 70, No. 2, 109-140 (2015).
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Discrete \(SL_{n}\)-connections and self-adjoint difference operators on 2-dimensional manifolds. (English. Russian original) Zbl 1282.39006

Russ. Math. Surv. 68, No. 5, 861-887 (2013); translation from Usp. Mat. Nauk 68, No. 5, 81-110 (2013).
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On deformations of linear differential systems. (English. Russian original) Zbl 1230.34080

Russ. Math. Surv. 66, No. 1, 63-105 (2011); translation from Usp. Mat. Nauk. 66, No. 1, 65-110 (2011).
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2D-Schrödinger operator, \((2+1)\) evolution systems and new reductions, 2D-Burgers hierarchy and inverse problem data. (English. Russian original) Zbl 1231.35199

Russ. Math. Surv. 65, No. 3, 580-582 (2010); translation from Uspekhi Mat. Nauk. 65, No. 3, 195-196 (2010).
MSC:  35Q53 37K10 35R30
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Topology and stability of integrable systems. (English. Russian original) Zbl 1202.37077

Russ. Math. Surv. 65, No. 2, 259-317 (2010); translation from Usp. Mat. Nauk 65, No. 2, 71-132 (2010).
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Abelian solutions of the soliton equations and Riemann-Schottky problems. (English. Russian original) Zbl 1164.37021

Russ. Math. Surv. 63, No. 6, 1011-1022 (2008); translation from Usp. Mat. Nauk 63, No. 6, 19-30 (2008).
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The Cauchy kernel for the Novikov-Dynnikov DN-discrete complex analysis in triangular lattices. (English. Russian original) Zbl 1141.39019

Russ. Math. Surv. 62, No. 4, 799-801 (2007); translation from Usp. Mat. Nauk 62, No. 4, 155-156 (2007).
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Functional equations defining multiplication in a continuous Krichever-Novikov basis. (English) Zbl 1152.47302

Russ. Math. Surv. 61, No. 1, 165-167 (2006); translation from Usp. Mat. Nauk 61, No. 1, 171-172 (2005).
MSC:  37K10 14H70 30D45 35Q58 37K20 39B32
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Highest-weight representations of Krichever-Novikov algebras and integrable systems. (English. Russian original) Zbl 1082.17012

Russ. Math. Surv. 60, No. 2, 370-372 (2005); translation from Usp. Mat. Nauk 60, No. 2, 177-178 (2005).
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The \(w\)-function of a solution of the \(g\)th stationary KdV equation. (English. Russian original) Zbl 1060.37054

Russ. Math. Surv. 58, No. 4, 780-781 (2003); translation from Usp. Mat. Nauk 58, No. 4, 145-146 (2003).
Reviewer: Ma Wen-Xiu (Tampa)
MSC:  37K10 35Q53 37K20
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Third-order commuting multidimensional differential operators that specify the KdV hierarchy. (English. Russian original) Zbl 1056.37509

Russ. Math. Surv. 58, No. 3, 610-612 (2003); translation from Usp. Mat. Nauk 58, No. 3, 187-188 (2003).
MSC:  37K10
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Formal series for the \(\tau\)-function realizing Riemann’s theorem about domains in the complex plane. (English. Russian original) Zbl 1114.37306

Russ. Math. Surv. 56, No. 4, 760-761 (2001); translation from Usp. Mat. Nauk 56, No. 4, 155-156 (2001).
MSC:  37K10 37K20
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Exactly integrable hyperbolic equations of Liouville type. (English. Russian original) Zbl 1003.35093

Russ. Math. Surv. 56, No. 1, 61-101 (2001); translation from Usp. Mat. Nauk 56, No. 1, 63-106 (2001).
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On an example of an integrable geodesic flow with positive topological entropy. (English. Russian original) Zbl 1058.37520

Russ. Math. Surv. 54, No. 4, 833-834 (1999); translation from Usp. Mat. Nauk 54, No. 4, 157-158 (1999).
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Obstructions for Seifert fibrations and an extension of the Bolsinov-Fomenko theorem on integrable Hamiltonian systems. (English. Russian original) Zbl 0978.37048

Russ. Math. Surv. 54, No. 3, 652-653 (1999); translation from Usp. Mat. Nauk 54, No. 3, 181-182 (1999).
MSC:  37J35 55S35 37J30 57N10 70H05
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Necessary and sufficient conditions for convergence of conditional mathematical expectations relative to a \(\sigma\)-algebra. (English. Russian original) Zbl 0946.60023

Russ. Math. Surv. 53, No. 6, 1358-1359 (1998); translation from Usp. Mat. Nauk 53, No. 6, 255-256 (1998).
MSC:  60F15 60F25
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Integrability by quadratures of Hamiltonian \(2n\)-dimensional systems with \(n\) known skew-orthogonal solutions. (English. Russian original) Zbl 0929.70014

Russ. Math. Surv. 53, No. 2, 380-381 (1998); translation from Usp. Mat. Nauk 53, No. 2, 143-144 (1998).
MSC:  70H06 37N05 37J35
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An algebraic formula for superposition and the completeness of the Bäcklund transformations of (2+1)-dimensional integrable systems. (English. Russian original) Zbl 0887.35144

Russ. Math. Surv. 51, No. 6, 1200-1202 (1996); translation from Usp. Mat. Nauk 51, No. 6, 197-198 (1996).
MSC:  35Q58 37J35 37K10 58J72
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Transversal intersection of separatrices, the structure of the set of quasi-stochastic motions and the non-existence of an analytic integral in multidimensional systems. (English. Russian original) Zbl 0877.58034

Russ. Math. Surv. 51, No. 4, 730-731 (1996); translation from Usp. Mat. Nauk 51, No. 4, 153-154 (1996).
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Complete integrability of generalized Knizhnik-Zamolodchikov equations of trigonometric type. (English. Russian original) Zbl 0873.17023

Russ. Math. Surv. 50, No. 3, 615-617 (1995); translation from Usp. Mat. Nauk 50, No. 3, 151-152 (1995).
Reviewer: A.Rudy (Minsk)
MSC:  17B67 35Q58 17B20
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The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body. (English. Russian original) Zbl 0881.58031

Russ. Math. Surv. 50, No. 3, 473-501 (1995); translation from Usp. Mat. Nauk 50, No. 3, 3-32 (1995).
Reviewer: D.Hurley (Cork)
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Abelian Bloch solutions of the two-dimensional Schrödinger equation. (English. Russian original) Zbl 0847.35091

Russ. Math. Surv. 50, No. 1, 195-197 (1995); translation from Usp. Mat. Nauk 50, No. 1, 191-192 (1995).
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A criterion for the topological conjugacy of Hamiltonian flows on two-dimensional compact surfaces. (English. Russian original) Zbl 0992.37500

Russ. Math. Surv. 50, No. 1, 193-194 (1995); translation from Usp. Mat. Nauk 50, No. 1, 189-190 (1995).
Reviewer: J.S.Joel (Kelly)
MSC:  37J35 70H05
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Canonical coordinates on orbits of the coadjoint representation of tensorial extensions of Lie groups. (English. Russian original) Zbl 0858.58018

Russ. Math. Surv. 49, No. 1, 251-253 (1994); translation from Usp. Mat. Nauk 49, No. 1(295), 229-230 (1994).
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The relative symplectic volume on orbits of a coadjoint representation of simple Lie groups. (English. Russian original) Zbl 0842.58036

Russ. Math. Surv. 48, No. 6, 185-186 (1993); translation from Usp. Mat. Nauk 48, No. 6(294), 173-174 (1993).
MSC:  37J99 37J35 37K10
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Topological analysis of a neighbourhood of a degenerate one-dimensional orbit of the Poisson action of \(\mathbb{R}^ 2\) on the symplectic manifold \(M^ 4\). (English. Russian original) Zbl 0834.58024

Russ. Math. Surv. 48, No. 6, 176-177 (1993); translation from Usp. Mat. Nauk 48, No. 6(294), 165-166 (1993).
MSC:  37J35 37K10 37J99 54H20
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Trajectory classification of integrable systems of Euler type in the dynamics of a rigid body. (English. Russian original) Zbl 0820.58029

Russ. Math. Surv. 48, No. 5, 165-166 (1993); translation from Usp. Mat. Nauk 48, No. 5(293), 163-164 (1993).
Reviewer: W.M.Oliva (Lisboa)
MSC:  37J35 37K10 37J99
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