Preprints
-
Abelian pole systems and Riemann-Schottky type systems.
(PDF: English,
arXiv: 2202.04585) 2022
-
Characterizing Jacobians of algebraic
curves with involution.(PDF: English,
arXiv: 2109.13161) 2021
Publications
-
Constrained Toda hierarchy and turning points of the Ruijsenaars-Schneider model.
(PDF: English,
arXiv: 2109.05240)
Lett. Math. Phys. 112(2) (2022), Paper No. 23, 26 pp.
(with A. Zabrodin).
-
Novikov-Veselov Symmetries of the Two-Dimensional
O(N) Sigma Model.
(PDF: English,
arXiv: 2106.14201)
SIGMA Symmetry Integrability Geom. Methods Appl. 18 (2022), Paper No. 006, 37 pp.
(with N. Nekrasov).
-
Kadomtsev-Petviashvili Turning Points and CKP Hierarchy.
(PDF: English,
arXiv: 2012.04482)
Comm. Math. Phys. 386(3) (2021), 1643–1683
(with A. Zabrodin).
-
Real-normalized differentials with a single order 2 pole.
(PDF: English,
arXiv: 2010.09358)
Lett. Math. Phys. 111(2) (2021), 36pp.
(with S. Lando and A. Skripchenko).
-
Towards Lefschetz Thimbles in Sigma Models, I.
(PDF: Russian, English,
arXiv: 2010.15575)
Soviet Phys. JETP 159:4 (2021), 822–844
(with N. Nekrasov).
-
Incarnations of XXX (slN)^ Bethe ansatz
equations and integrable hierarchies.
(PDF: English,
arXiv: 1907.12198)
Proc. Sympos. Pure Math 103
(2021), 239–295
(with A. Varchenko).
-
Real-normalized differentials: limits on stable curves.
(PDF: Russian, English,
arXiv: 1703.07806)
Uspekhi Mat. Nauk 74:2(446)
(2019), 81–148
(with S. Grushevsky and C. Norton).
-
Two-Dimensional Periodic Schrödinger Operators
Integrable at an Energy Eigenlevel. (PDF: Russian, English,
arXiv: 1903.01778)
Funktsional. Anal. i Prilozhen. 53:1
(2019), 31–48
(with A. Ilina and N. Nekrasov).
-
Triangular reductions of the 2D Toda hierarchy. (PDF: Russian, English,
arXiv: 1609.05120)
Funktsional. Anal. i Prilozhen. 51:1
(2017), 48–65 (with A. Ilina).
-
Real-normalized differentials and the elliptic Calogero-Moser system. (PDF: English,
arXiv: 1108.4211)
Complex geometry and dynamics, Abel Symp.
10 (2015), 123–137
(with S. Grushevsky).
-
Commuting difference operators and the combinatorial Gale transform. (PDF: English,
arXiv: 1403.4629)
Funktsional. Anal. i Prilozhen., translation in Funct. Anal. Appl.
49(3) (2015), 22–40.
-
Amoebas, Ronkin function, and Monge-Ampère measures of
algebraic curves with marked points. (PDF: English,
arXiv: 1310.8472)
Topology, geometry, integrable systems, and mathematical
physics, Amer. Math. Soc. Transl. Ser. 2
234 (2014), 265–278
- Soliton equations and the Riemann-Schottky problem.
(PDF: English,
arXiv: 1111.0164)
Handbook of moduli. Vol. II,
Adv. Lect. Math. (ALM)
(2013), 205–258
(with T. Shiota).
-
Real normalized differentials and Arbarello's conjecture.
(PDF: English,
arXiv: 1112.6427)
Funktsional. Anal. i Prilozhen., translation in Funct. Anal. Appl.
46(2) (2012), 110–120
-
A note on critical
points of integrals of soliton equations. (PDF: English,
arXiv: 1005.3741)
Anal. Math. Phys. 1:1 (2011), 15–35
(with D. Zakharov).
-
Abelian solutions of
the soliton equations and geometry of abelian varieties.
(PDF: English,
arXiv: 0804.0794)
Liaison, Schottky problem and
invariant theory, Progr. Math. 280 (2010), 197–222 (with T. Shiota).
- Characterizing Jacobians via trisecants of the Kummer
Variety. (PDF: English,
arXiv: math/0605625)
Ann. of Math. (2) 172:1 (2010), 485–516.
-
Integrable discrete Schrödinger equations and a
characterization of Prym varieties by a pair of
quadrisecants. (PDF: English,
arXiv: 0705.2829)
Duke Math. J. 152:2 (2010), 317–371 (with S. Grushevsky).
-
The universal Whitham
hierarchy and the geometry of the moduli space of
pointed Riemann surfaces. (PDF: English,
arXiv: 0810.2139)
Surv. Differ. Geom. 14 (2009), 111–129 (with S. Grushevsky).
-
Abelian solutions of the soliton equations and
Riemann-Schottky problems. (PDF: English)
Uspekhi Mat. Nauk 63:6(384) (2008), 19–30.
- Seiberg-Witten Theory,
Symplectic Forms, and Hamiltonian Theory of Solitons.
(PDF: English,
arXiv: hep-th/0212313)
Superstring theory, Adv. Lect. Math.
(ALM) 1 (2008), 124–177
(with E. D'Hoker and D.H. Phong).
- Abelian solutions of
the KP equation.
(PDF: English,
arXiv: 0804.0274)
Geometry, topology, and mathematical
physics, Amer. Math. Soc. Transl. Ser. 2 224 (2008),
173–191 (with T. Shiota).
- On
the scaling limit of a singular integral operator.
(PDF: English,
arXiv: 0708.4157)
Geom. Dedicata 132 (2008),
121–134 (with D.H. Phong).
-
Lax operator algebras. (PDF: Russian, English,
arXiv: math/0701648)
Funktsional. Anal. i Prilozhen. 41:4
(2007), 46–59 (with O.K. Sheinman).
- A
characterization of Prym varieties. (PDF: English, arXiv: math/0506238)
Int. Math. Res. Not. Art. ID 81476 (2006), 36pp
.
-
Integrable equations, addition theorems, and the Riemann-Schottky
problem. (PDF: Russian, English)
Uspekhi Mat. Nauk 61:1 (2006), 25–84 (with V.M. Bukhshtaber).
- Integrable linear equations and the Riemann-Schottky
problem. (PDF: English,
arXiv: math/0504192)
Algebraic geometry and number theory,
Progr. Math. 253 (2006), 497–514.
-
Conformal mappings and the Whitham equations. (PDF: English)
Surveys in modern mathematics, London
Math. Soc. Lecture Note Ser. Cambridge Univ. Press (2005), 316–327
.
-
Characterizing Jacobians via flexes of the Kummer
Variety. (PDF: English,
arXiv: math/0502138)
Math. Res. Lett. 13:1 (2006), 109–123 (with E. Arbarello and G. Marini).
-
Algebraic versus Liouville integrability of the
soliton systems. (PDF: English)
XIVth International Congress on
Mathematical Physics World
Sci. Publ (2005), 50–67
.
-
Integrable Structure of the Dirichlet Boundary Problem
in Multiply-Connected Domains. (PDF: English,
arXiv: hep-th/0309010)
Comm. Math. Phys. 259:1 (2005), 1–44 (with A. Marshakov and A. Zabrodin).
-
Analytic theory of difference equations with rational and
elliptic coefficients and the Riemann-Hilbert problem.
(PDF: Russian,
English,
arXiv: math-ph/0407018)
Uspekhi Mat. Nauk 59:6 (2004), 111–150.
-
Laplacian growth and Whitham equations of soliton theory.
(PDF: English,
arXiv: nlin/0311005)
Phys. D 198:1–2
(2004), 1–28
(with M. Mineev-Weinstein, P.
Wiegmann, and A. Zabrodin).
-
Integrable chains on
algebraic curves. (PDF: English,
arXiv: hep-th/0309255)
Geometry, topology, and mathematical
physics, Amer. Math. Soc. Transl. Ser. 2 212 (2004), 219–236.
-
Two-dimensionalized Toda lattice, commuting difference operators,
and holomorphic bundles.
(PDF: Russian, English,
arXiv: math-ph/0308019)
Uspekhi Mat. Nauk 58:3 (2003), 51–88 (with S.P. Novikov).
-
Elliptic families of solutions of the Kadomtsev-Petviashvili
equation, and the field analogue of the elliptic
Calogero-Moser system. (PDF: Russian, English,
arXiv: hep-th/0203192)
Funktsional. Anal. i Prilozhen. 36:4 (2002), 1–17 (with A.A. Akhmetshin and Yu.S. Volvovski).
-
Spin chains with twisted monodromy. (
PDF: English, arXiv: hep-th/0110098)
J. Inst. Math. Jussieu 1:3 (2002), 477–492 (with D.H. Phong).
-
Isomonodromy equations on algebraic curves, canonical
transformations and Whitham equations.
(PDF: English,
arXiv: hep-th/0112096)
Mosc. Math. J. 2:4 (2002), 717–752
-
Vector
bundles and Lax equations on algebraic curves.
(PDF: English,
arXiv: hep-th/0108110)
Comm. Math. Phys. 229:2 (2002), 229–269.
- The periodic and open
Toda lattice. (PDF: English,
arXiv: hep-th/0010184)
Mirror symmetry, IV (Montreal, QC,
2000), AMS/IP Stud. Adv. Math. 33 (2002),
139–158 (with K.L. Vaninsky).
-
The τ-function for analytic curves.
(PDF: English,
arXiv: hep-th/0005259)
Random matrix models and their
applications, Math. Sci. Res. Inst. Publ. 40 (2000),
285–299 (with I.K. Kostov, M. Mineev-Weinstein, P.
Wiegmann, and A. Zabrodin).
-
Holomorphic bundles and commuting difference operators. Two-point
constructions. (PDF: Russian, English)
Uspekhi Mat. Nauk 55:3(333) (2000),
181–182 (with S.P. Novikov).
-
Holomorphic bundles and difference scalar operators: single-point
constructions. (PDF: Russian, English,
arXiv: math-ph/0004008)
Uspekhi Mat. Nauk 55:1(331) (2000),
187–188 (with S.P. Novikov).
- Spin
chain models with spectral curves from M theory.
(PDF: English,
arXiv: hep-th/9912180)
Comm. Math. Phys. 213:3 (2000),
539–574 (with D.H. Phong).
-
Elliptic analog of the Toda lattice. (PDF: English,
arXiv: hep-th/9909224)
Internat. Math. Res. Notices 8 (2000), 383–412.
- Baker-Akhiezer
functions and integrable systems.
(PDF: English)
Integrability: The Seiberg-Witten and
Whitham equations Gordon
and Breach (2000), 1–22.
-
Elliptic solutions to
difference nonlinear equations and nested Bethe ansatz
equations. (PDF: English,
arXiv: solv-int/9804016)
Calogero-Moser-Sutherland models
(Montréal, QC, 1997) CRM Ser. Math. Phys. Springer
(2000), 249–271.
-
Trivalent graphs and solitons. (PDF: Russian, English, arXiv: math-ph/0004009)
Uspekhi Mat. Nauk 54:6(330) (1999), 149–150 (with S.P. Novikov).
-
Periodic and almost-periodic potentials in inverse problems.
(PDF: English,
arXiv: math-ph/0003004)
Inverse Problems 15:6 (1999), 117–144 (with S.P. Novikov).
-
A generating formula for solutions of associativity
equations. (PDF: Russian, English,
arXiv: hep-th/9904028)
Uspekhi Mat. Nauk 54:2(326) (1999),
167–168 (with A.A. Akhmetshin and Yu.S. Volvovski).
-
Discrete analogues of the Darboux-Egorov metrics.
(PDF: Russian, English,
arXiv: hep-th/9905168)
Tr. Mat. Inst. Steklova 255 (1999), 21–45 (with A.A. Akhmetshin and Yu.S. Volvovski).
-
Vacuum curves of
elliptic L-operators and representations of Sklyanin
algebra. (PDF: English,
arXiv: solv-int/9801022)
Moscow Seminar in Mathematical
Physics Amer. Math. Soc.
Transl. Ser. 2 (1999), 199–221 (with A. Zabrodin).
-
Symplectic forms in
the theory of solitons. (PDF: English,
arXiv: hep-th/9708170)
Surveys in differential geometry:
integral systems Int.
Press, Boston, MA (1998), 239–313 (with D.H. Phong).
-
Elliptic solutions to difference non-linear equations
and related many-body problems. (PDF: English,
arXiv: hep-th/9704090)
Comm. Math. Phys. 193:2 (1998),
373–396 (with P. Wiegmann and A. Zabrodin).
-
Solitons in high-energy QCD. (PDF: English,
arXiv: hep-th/9704079)
Nuclear Physics B 505:1–2 (1997),
387–414 (with G.P. Korchemsky).
-
Algebraic-geometric n-orthogonal curvilinear coordinate
systems and the solution of associativity equations.
(PDF: Russian, English,
arXiv: hep-th/9611158)
Funktsional. Anal. i Prilozhen. 31:1 (1997),
32–50.
-
The renormalization group equation in
N=2 supersymmetric gauge theories. (PDF: English,
arXiv: hep-th/9610156)
Nuclear Phys. B 494:1–2 (1997),
89–104 (with E. D'Hoker and D.H. Phong).
-
The effective prepotential of N=2 supersymmetric SO(Nc) and
Sp(Nc) gauge theories.
(PDF: English,
arXiv: hep-th/9609145)
Nuclear Phys. B 489:1–2 (1997),
211–222 (with E. D'Hoker and D.H. Phong).
-
The effective prepotential of N=2 supersymmetric SU(Nc) gauge theories. (PDF: English,
arXiv: hep-th/9609041)
Nuclear Phys. B 489:1–2 (1997), 197–210 (with E. D'Hoker and D.H. Phong).
-
Quantum integrable models and discrete classical
Hirota equations. (PDF: English)
Comm. Math. Phys. 188:2 (1997), 267–304 (with O. Lipan, P. Wiegmann, and A. Zabrodin).
-
On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories. (PDF: English,
arXiv: hep-th/9604199)
J. Differential Geom. 45:N2 (1997), 349–389 (with D.H. Phong).
- Quantum integrable
systems and classical discrete nonlinear dynamics.
(PDF: English,
arXiv: hep-th/9604080)
Statistical models, Yang-Baxter
equation and related topics, and Symmetry, statistical
mechanical models and applications (Tianjin, 1995) World Sci. Publ., River Edge, NJ
(1996), 211–227 (with O. Lipan, P. Wiegmann, and
A. Zabrodin).
-
Multidimensional vector addition theorems and the
Riemann theta functions. (PDF: English)
Internat. Math. Res. Notices 10 (1996), 505–513 (with V. Buchstaber).
- Integrability and Seiberg-Witten exact solution. (PDF: English, arXiv: hep-th/9505035)
Phys. Lett. B 355:3–4 (1995), 466–474 (with A. Gorsky, A. Marshakov, A. Mironov,
and A. Morozov).
-
Spin generalization of the Ruijsenaars-Schneider model, the
non-Abelian 2D Toda chain, and representations of the
Sklyanin algebra. (PDF: Russian, English,
arXiv: hep-th/9505039)
Uspekhi Mat. Nauk 50:6(306) (1995), 3–56 (with A. Zabrodin).
- Algebraic-geometrical methods in the theory of
integrable equations and their perturbations.
(PDF: English)
Acta Appl. Math. 39:1–3 (1995), 93–125.
- Linear operators with self-consistent coefficients and
rational reductions of KP hierarchy. (PDF: English)
Phys. D 87:1–4 (1995), 14–19.
-
Spin generalization of
the Calogero-Moser system and the matrix KP equation.
(PDF: English,
arXiv: hep-th/9411160)
Amer. Math. Soc. Transl. Ser. 2 170
(1995), 83–119 (with O. Babelon, E. Billey, M. Talon).
- Finite genus solutions to the Ablowitz-Ladik equations.
(PDF: English)
Comm. Pure Appl. Math. 48:12 (1995), 1369–1440 (with P.D Miller, N.M. Ercolani, and C.D.
Levermore).
-
General rational reductions of the Kadomtsev-Petviashvili
hierarchy and their symmetries. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 29:2
(1995), 1–8.
- Elliptic solutions of nonlinear
integrable equations and related topics.
(PDF: English)
Acta Appl. Math. 36:1–2 (1994), 7–25
.
-
Two-dimensional algebraic-geometric operators with self-consistent
potentials. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 28:1
(1994), 26–40.
-
The τ-function of the
universal Whitham hierarchy, matrix models and
topological field theories. (PDF: English,
arXiv: hep-th/9205110)
Comm. Pure Appl. Math. 47:4 (1994), 437–475.
-
Vector addition theorems and Baker-Akhiezer functions.
(PDF: Russian, English)
Teoret. Mat. Fiz. 94:2 (1993), 200–212 (with V.M. Bukhshtaber).
- The Cauchy problem for
doubly periodic solutions of KP-II equation.
(PDF: English)
Important developments in soliton
theory Springer (1993), 123–146.
- Perturbation Theory in
Periodic Problems for Two-Dimensional Integrable Systems.
Sov. Sci. Rev., Sect. C, Math. Phys.
Rev. 9:2 (1992), 1–103.
- Whitham theory for
integrable systems and topological quantum field
theories.
(PDF: English)
New symmetry principles in quantum
field theory (Cargèse, 1991) Plenum (1992), 309–327
.
- The dispersionless Lax equations and topological
minimal models. (PDF: English)
Comm. Math. Phys. 143:2 (1992), 415–429.
-
Multiphase solutions of the Benjamin-Ono equation and their
averaging. (PDF: Russian, English)
Mat. Zametki 49:6 (1991), 42–58 (with S.Yu. Dobrokhotov).
- The periodic problems
for two-dimensional integrable systems.
(PDF: English)
Proceedings of the International
Congress of Mathematicians, Vol. I, II (Kyoto, 1990) Math. Soc. Japan, Tokyo (1991), 1353–1362.
- The averaging
procedure for the soliton-like solutions of integrable
systems. (PDF: English)
Mechanics, analysis and geometry: 200
years after Lagrange North-Holland (1991), 99–125.
- Riemann surfaces, operator fields, strings. Analogues of the
Fourier-Laurent bases. (PDF: English)
Physics and mathematics of strings World Scientific (1990), 356–388 (with S.P. Novikov).
-
Generalized elliptic genera and Baker-Akhiezer functions.
(PDF: Russian, English)
Mat. Zametki 47:2 (1990), 34–45.
- On Heisenberg
relations for the ordinary linear differential operators.
ETH Zürich preprint (1990).
-
Spectral
theory of two-dimensional periodic operators and its
applications. (PDF: Russian, English)
Uspekhi Mat. Nauk 44:2(266) (1989), 121–184.
-
Algebras of Virasoro type, the energy-momentum tensor, and
operator expansions on Riemann surfaces.
(PDF: Russian,
English)
Funktsional. Anal. i Prilozhen. 23:1
(1989), 24–40 (with S.P. Novikov).
- Algebraic-geometry
methods in soliton theory.
Soliton theory: a survey of results.,
Nonlinear Sci. Theory Appl., Chapter 14 (1990),
354–400 (with P.G. Grinevich).
- New method of finding dynamic solutions in the Peierls
model. (PDF: English)
Soviet Phys. JETP 94:7 (1988), 344–354 (with I.E. Dzyaloshinskii, J. Chronek).
-
A periodic problem for
the Kadomtsev-Petviashvili equation.
(PDF: Russian)
Dokl. Akad. Nauk SSSR 298:4 (1988), 802–807
.
- Virasoro-Gelfand-Fuks type algebras, Riemann surfaces,
operator's theory of closed strings. (PDF: English)
J. Geom. Phys. 5:4 (1988), 631–661 (with S.P. Novikov).
- Exact solutions of the time-dependent Schrödinger
equation with self-consistent potentials.
(PDF: Russian)
Soviet J. Particles and Nuclei 19:3
(1988), 579–621 (with B.A. Dubrovin, T.M. Malanyuk, V.G.
Makhan'kov).
-
The averaging method for two-dimensional "integrable"
equations. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 22:3
(1988), 37–52.
-
Evolution of the
Whitham zone in the Korteweg-de Vries theory.
(PDF: Russian,
English)
Dokl. Akad. Nauk SSSR 295:2 (1987),
345–349 (with V.V. Avilov, S.P. Novikov).
-
Algebras of Virasoro type, Riemann surfaces and strings in
Minkowski space. (PDF: Russian,
English)
Funktsional. Anal. i Prilozhen. 21:4
(1987), 47–61 (with S.P. Novikov).
-
Algebras of Virasoro type, Riemann surfaces and the structures
of soliton theory. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 21:2 (1987),
46–63 (with S.P. Novikov).
-
The spectral theory of "finite-gap" nonstationary
Schrödinger operators. The nonstationary Peierls
model. (PDF: Russian,
English)
Funktsional. Anal. i Prilozhen. 20:3
(1986), 42–54
- Wess-Zumino Lagrangians in chiral models and
quantization of their constants. (PDF: English)
Nuclear Phys. B 264:2–3 (1986), 415–422 (with M.A. Olshanetsky, A.M. Perelomov).
-
Rational multisoliton
solutions of the nonlinear Schrödinger equation.
(PDF: Russian)
Dokl. Akad. Nauk SSSR 287:3 (1986), 606–610 (with V.M. Eleonskii, N.E. Kulagin).
- Algebraic-geometrical
methods in some problems of solid state physics.
Proc. int. conf Dubna (1985).
- Two-dimensional
periodic Schrödinger operators and Prym's
θ-functions. (PDF: English)
Geometry today (Rome, 1984), Progr.
Math., 60 (1985), 283–301
(with A.P. Veselov, S.P. Novikov).
-
Integrable systems. I. (PDF: Russian)
Itogi Nauki i Tekhniki, Akad. Nauk
SSSR, VINITI, Dynamical
Systems 4 (1985), 179–277 (with B.A. Dubrovin, S.P. Novikov).
-
Two-dimensional
periodic difference operators and algebraic geometry
(PDF: Russian).
Dokl. Akad. Nauk SSSR 285:1 (1985),
31–36
.
-
The Laplace method, algebraic curves and nonlinear
equations. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 18:3
(1984), 43–56.
-
Nonlinear equations and elliptic curves. (PDF: Russian, English)
Itogi Nauki i Tekhniki, Akad. Nauk
SSSR, VINITI, 23 (1983), 79–136.
-
Sound
and charge-density wave in the discrete Peierls model.
(PDF: English)
JETP 58:5 (1983),
1031–1040 (with I.E. Dzyaloshinskii).
-
The "Hessian" of
integrals of the Korteweg-de Vries equation and
perturbations of finite-gap solutions.
(PDF: Russian)
Dokl. Akad. Nauk SSSR 270:6 (1983), 1312–1317.
- Algebraic geometry
methods in the theory of the Baxter-Yang equations.
Soviet Science Reviews, Math. Phys.
Rev. 3 (1982), 53–81.
- Topological and
algebraic-geometrical methods in contemporary
mathematical physics.
Soviet Science Reviews, Math. Phys.
Rev. 3 (1982), 1–151
(with B.A. Dubrovin, S.P. Novikov).
-
Spectral theory of difference operators, algebraic geometry, and the Peiers model.
(I.G. Petrovski seminar on differential equations and mathematical problems in physics).
(PDF: Russian)
Uspehi Mat. Nauk 37:2(224) (1982), 259–260.
-
The Peierls model. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 16:4
(1982), 10–26.
-
Commensurability
effects in the discrete Peierls model.
(PDF: English)
Soviet Phys. JETP 56:4 (1982),
908–913 (with I.E. Dzyaloshinskii).
- Exactly soluble Peierls models. (PDF: English)
Phys. Let A 91:1 (1982), 40–42 (with S.A Brazovskii, I.E. Dzyaloshinskii).
-
Discrete Peierls models with exact solutions.
(PDF: English)
Soviet Phys. JETP 56:1 (1982), 212–225
(with S.A Brazovskii, I.E. Dzyaloshinskii).
-
Algebro-geometric
spectral theory of the Schrödinger difference
operator and the Peierls model.
(PDF: Russian)
Dokl. Akad. Nauk SSSR 265:5 (1982), 1054–1058.
-
The spectral theory of difference operators, algebraic
geometry, and Peierls model
(I.G. Petrovski seminar on differential equations and mathematical problems in physics). (PDF: Russian)
Uspekhi Mat. Nauk 37:2(224) (1982), 259–260.
- Holomorphic bundles and nonlinear equations.
(PDF: English)
Physica D: Nonlinear Phenomena 3:1–2
(1981), 267–293 (with S.P. Novikov).
-
The Baxter equations and algebraic geometry.
(PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 15:2 (1981),
22–35.
-
The periodic non-Abelian Toda chain and its
two-dimensional generalization (Appendix to B.A. Dubrovin,
Theta functions and non-linear equations). (PDF: Russian, English)
Uspekhi Mat. Nauk 36:2(218) (1981), 72–77.
-
Elliptic solutions of the Kadomcev-Petviašvili equations, and
integrable systems of particles. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 14:4 (1980),
45–54.
-
Holomorphic bundles over algebraic curves, and nonlinear equations.
(PDF: Russian, English)
Uspekhi Mat. Nauk 35:6(216) (1980), 47–68 (with S.P. Novikov).
-
Self-similar solutions of equations of Korteweg-de Vries type.
(PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 14:3 (1980),
83–84.
-
An analogue of the
d'Alembert formula for the equations of a principal
chiral field and the sine-Gordon equation.
(PDF: Russian)
Dokl. Akad. Nauk SSSR 253:2 (1980), 288–292.
- The inverse problem
method and holomorphic bundles on Riemann surfaces.
Soviet Sci. Rev. Sect. C: Math. Phys.
Rev. 1 (1980), 5–26 (with S.P. Novikov).
- Methods of algebraic
geometry in contemporary mathematical physics.
Soviet Sci. Rev. Sect. C: Math.
Phys. Rev. 1 (1980), 1–54 (with V.G. Drinfel'd, Yu.I.
Manin, S.P. Novikov).
-
On the rational solutions of the Zaharov-Šabat equations
and completely integrable systems of N particles on the line. (PDF: Russian, English).
Zap. Nauchn. Sem. Leningrad. Otdel.
Mat. Inst. Steklov. (LOMI) 84 (1979), 117–130
.
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Rational solutions of duality equations for Yang-Mills fields.
(PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 13:4 (1979),
81–82.
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Holomorphic bundles
and nonlinear equations. Finite-gap solutions of rank 2.
(PDF: Russian, English)
Dokl. Akad. Nauk SSSR 247:1 (1979), 33–37 (with S.P. Novikov).
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Holomorphic bundles and the Kadomcev-Petviašvili equation
(I.G. Petrovski seminar on differential equations and mathematical problems in physics).
(PDF: Russian)
Uspehi Mat. Nauk 33:5(203) (1978), 209–211. (with S.P. Novikov)
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Algebraic curves and nonlinear difference equations.
(PDF: Russian, English)
Uspekhi Mat. Nauk 33:4(202) (1978), 215–216.
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Holomorphic vector bundles over Riemann surfaces and the
Kadomcev-Petviašvili equation. I. (PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 12:4 (1978), 41–52 (with S.P. Novikov).
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Commutative rings of ordinary linear differential operators.
(PDF: Russian, English)
Funktsional. Anal. i Prilozhen. 12:3 (1978), 20–31
.
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Rational solutions of the Kadomcev-Petviašvili equation
(I.G. Petrovski seminar on differential equations and mathematical problems in physics).
(PDF: Russian)
Uspehi Mat. Nauk 33:2(200) (1978), 227–228.
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Rational solutions of the Kadomcev-Petviašvili equation
and the integrable systems of N particles on a line.
(PDF: Russian, English)
Funkcional. Anal. i Priložen. 12:1 (1978), 76–78.
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Methods of algebraic geometry in the theory of nonlinear
equations. (PDF: Russian, English)
Uspehi Mat. Nauk 32:6(198) (1977), 183–208.
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Geometry of Riemann surfaces and non-linear differential
equations (I.G. Petrovski seminar on differential equations and mathematical problems in physics). (PDF: Russian)
Uspehi Mat. Nauk 32:1(193) (1977), 229–230 (with B.A. Dubrovin).
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Integration of nonlinear equations by the methods of algebraic
geometry. (PDF: Russian, English)
Funkcional. Anal. i Priložen 11:1 (1977), 15–31.
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Algebraic curves and commuting matrix differential operators.
(PDF: Russian, English)
Funkcional. Anal. i Priložen 10:2 (1976), 75–76.
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The Schrödinger
equation in a periodic field and Riemann surfaces.
(PDF: Russian, English)
Dokl. Akad. Nauk SSSR 229:1 (1976), 15–18 (with B.A. Dubrovin, S.P. Novikov).
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An
algebraic-geometric construction of the Zaharov-Šabat
equations and their periodic solutions.
(PDF: Russian)
Dokl. Akad. Nauk SSSR
227:2 (1976), 291–294.
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Obstructions to the existence of S1-actions.
Bordisms of branched coverings. (PDF: Russian, English)
Izv. Akad. Nauk SSSR Ser. Mat. 40:4
(1976), 828–844.
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Potentials with zero coefficient of reflection against a
background of the finite zone potentials.
(PDF: Russian, English)
Funkcional. Anal. i Priložen 9:2 (1975), 77–78
.
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Equivariant Hirzebruch genera. The Atiya-Hirzebruch formula.
(PDF: Russian)
Uspehi Mat. Nauk 30:1(181) (1975), 243–244.
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Formal groups and the Atiyah-Hirzebruch formula.
(PDF: Russian, English)
Izv. Akad. Nauk SSSR 38:6, (1974), 1289–1304.
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A remark on the paper "Actions of finite cyclic groups
on quasicomplex manifolds'' .
(PDF: Russian,
English)
Mat. Sb. (N.S.). 95(137):1(9) (1974), 146–147.
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The invariance of the characteristic classes for the
manifolds of the homotopy type of CP(n).
(PDF: Russian)
Uspehi Mat. Nauk 28:5(173) (1973), 245–246.
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Actions of finite cyclic groups on quasicomplex manifolds.
(PDF: Russian, English)
Mat. Sb. (N.S.). 90(132):2 (1973), 306–319.
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Formulae for the fixed points of an action of the group
Zp.
(PDF: Russian)
Uspehi Mat. Nauk 28:1(169) (1973), 237–238 (with S.M. Gusein-Zade).
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Bordisms of groups acting freely on spheres.
(PDF: Russian)
Uspehi Mat. Nauk 26:6(162) (1971), 245–246.