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SIGMA 3 (2007), 074, 6 pages arXiv:0706.3387
https://doi.org/10.3842/SIGMA.2007.074
Contribution to the Vadim Kuznetsov Memorial Issue
Vadim Kuznetsov. Informal Biography by Eyes of His First Adviser
Igor V. Komarov
St. Petersburg State University, St. Petersburg, Russia
Received May 20, 2007; Published online June 22, 2007
Abstract
The paper is dedicated to the memory of prominent theoretical physicist and
mathematician Dr. Vadim Kuznetsov who worked, in particular, in the fields of the
nonlinear dynamics, separation of variables, integrability theory, special functions. It includes
his short research biography, an account of the start of his research career and the list of publications.
Key words:
classical and quantum integrable systems; separation of variables.
pdf (162 kb)
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Dr. Vadim B. Kuznetsov: List of publications
-
Komarov I.V., Kuznetsov V.B., Quasiclassical quantization of the
Kowalevski top,
Teoret. Mat. Fiz. 73 (1987), 335-347
(English transl.: Theor. and Math. Phys. 73 (1987),
1255-1263).
-
Komarov I.V., Kuznetsov V.B., The generalized Goryachev-Chaplygin gyrostat in quantum mechanics,
in Differentsialnaya Geom. Gruppy Li i Mekh., Vol. IX,
Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 164 (1987), 133-141, 198
(English transl.: J. Soviet Math. 47 (1989), no. 2, 2459-2466).
-
Bobenko A.I., Kuznetsov V.B., Lax representation and new formulae
for the Goryachev-Chaplygin top, J. Phys. A: Math. Gen. 21
(1988), 1999-2006.
- Kuznetsov V.B., Tsiganov A.V., A special case of Neumann's system
and the Kowalevski-Chaplygin-Goryachev top, J. Phys. A: Math. Gen.
22 (1989), L73-L79.
- Kuznetsov V.B., Tsiganov A.V., Infinite series of Lie algebras and boundary conditions for
integrable systems, in Differentsialnaya Geom. Gruppy Li i Mekh., Vol. 10, Zapiski Nauchn. Sem. LOMI 172 (1992), 88-98, 170
(English transl.: J. Soviet Math. 59 (1992), no. 5, 1085-1092).
- Komarov I.V., Kuznetsov V.B., Kowalevski's top on the Lie algebras
o(4), e(3), and o(3,1), J. Phys. A: Math. Gen. 23 (1990),
841-846.
- Kuznetsov V.B., Generalized polyspheroidal periodic functions and
the quantum inverse scattering method, J. Math. Phys. 31 (1990),
1167-1174.
- Komarov I.V., Kuznetsov V.B., Quantum Euler-Manakov top on the 3-sphere
S3, J. Phys. A: Math. Gen. 24 (1991), L737-L742.
-
Kuznetsov V.B., On the equivalence of two families of quantum integrable systems,
in Voprosy Kvant. Teor. Polya Statist. Fiz., Vol. 11, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)
Vol. 199 (1992), 114-131, 186
(English transl.: J. Math. Sci. 77 (1995), no. 2, 3090-3101).
- Kuznetsov V.B., Quadrics on Riemannian spaces of constant curvature. Separation of variables and a connection with the Gaudin magnet, Teoret. Mat. Fiz. 91 (1992), no. 1, 83-111
(English transl.: Theoret. and Math. Phys. 91 (1992), no. 1, 385-404).
- Kuznetsov V.B., Quadrics on real Riemannian spaces of constant curvature:
separation of variables and connection with Gaudin magnet,
J. Math. Phys. 33 (1992), 3240-3254.
- Kuznetsov V.B., On isomorphism of n-dimensional Neumann system
and n-site Gaudin magnet,
Funktsional. Anal. i Prilozhen. 26 (1992), no. 4, 88-90
((English transl.: Funct. Anal. Appl. 26 (1992), no. 4, 302-304).
- Kuznetsov V.B., Equivalence of two graphical calculi,
J. Phys. A: Math. Gen. 25 (1992), 6005-6026.
- Enol'skii V.Z., Kuznetsov V.B., Salerno M., On the quantum inverse scattering
method for the DST dimer, Phys. D 68 (1993), 138-152.
- Eilbeck J.C., Enol'skii V.Z., Kuznetsov V.B., Leykin D.V.,
Linear r-matrix algebra for systems separable in parabolic
coordinates, Phys. Lett. A 180 (1993), 208-214.
- Christiansen P.L., Jørgensen M.F., Kuznetsov V.B., On integrable systems
close to the Toda lattice, Lett. Math. Phys. 29 (1993), 165-173.
- Kuznetsov V.B.; Tsyganov A.V., Quantum relativistic Toda
lattices, in Differentsialnaya Geom. Gruppy
Li i Mekh., Vol. 13, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat.
Inst. Steklov. (POMI) 205 (1993), 71-84, 180
(English transl.: J. Math. Sci. 80
(1996), no. 3, 1802-1810).
- Koornwinder T.H., Kuznetsov V.B., Gauss hypergeometric function and quadratic
R-matrix algebras, Algebra i Analiz 6 (1994), 161-184
(English transl.: St. Petersburg Math. J. 6 (1995), 595-618),
hep-th/9311152.
- Kalnins E.G., Kuznetsov V.B., Miller W.Jr., Quadrics on complex Riemannian
spaces of constant curvature, separation of variables and the Gaudin magnet,
J. Math. Phys. 35 (1994), 1710-1731, hep-th/9308109.
- Eilbeck J.C., Enol'skii V.Z., Kuznetsov V.B., Tsiganov A.V., Linear r-matrix
algebra for classical separable systems, J. Phys. A: Math. Gen.
27 (1994), 567-578, hep-th/9306155.
- Eilbeck J.C., Enol'skii V.Z., Kuznetsov V.B., Leykin D.V., Classical Poisson
structure for a hierarchy of one-dimensional particle systems separable in
parabolic coordinates, J. Nonlinear Math. Phys. 1 (1994),
275-294.
- Kalnins E.G., Kuznetsov V.B., Miller W.Jr., Separation of variables and XXZ
Gaudin magnet, Rend. Sem. Mat. Univ. Politec. Torino 53 (1995), 109-120,
hep-th/9412190.
- Kuznetsov V.B., Jørgensen M.F., Christiansen P.L., New boundary conditions for
integrable lattices, J. Phys. A: Math. Gen. 28 (1995),
4639-4654, hep-th/9503168.
- Kuznetsov V.B., Sklyanin E.K., Separation of variables in A2 type Jack
polynomials, RIMS Kokyuroku 919 (1995), 27-43, solv-int/9508002.
- Kuznetsov V.B., 3F2(1) hypergeometric function and quadratic R-matrix algebra,
in Symmetries and Integrability of difference equations (Esterel, PQ, 1994),
CRM Proc. Lecture Notes, Vol. 9, Amer. Math. Soc., Providence, RI, 1996,
185-197, hep-th/9410146.
- Nijhoff F.W., Ragnisco O., Kuznetsov V.B., Integrable time-discretization of the
Ruijsenaars-Schneider model, Comm. Math. Phys. 176 (1996),
681-700, hep-th/9412170.
- Kuznetsov V.B., Hidden symmetry of the quantum Calogero-Moser system,
Phys. Lett. A 218 (1996), 212-222, solv-int/9509001.
- Kuznetsov V.B., Sklyanin E.K., Separation of variables for the A2 Ruijsenaars
system and a new integral representation for the A2 Macdonald polynomials,
J. Phys. A: Math. Gen. 29 (1996), 2779-2804, q-alg/9602023.
- Nijhoff F.W., Kuznetsov V.B., Sklyanin E.K., Ragnisco O., Dynamical r-matrix
for the elliptic Ruijsenaars-Schneider system, J. Phys. A: Math. Gen.
29 (1996), L333-L340, solv-int/9603006.
- Kuznetsov V.B., Separation of variables for the Dn type periodic Toda
lattice, J. Phys. A: Math. Gen. 30 (1997), 2127-2138, solv-int/9701009.
- Kuznetsov V.B., Nijhoff F.W., Sklyanin E.K., Separation of variables for the
Ruijsenaars system, Comm. Math. Phys. 189 (1997), 855-877, solv-int/9701004.
- Kuznetsov V.B., Sklyanin E.K., On Bäcklund transformations
for many-body systems, J. Phys. A: Math. Gen. 31 (1998),
2241-2251, solv-int/9711010.
- Kuznetsov V.B., Sklyanin E.K., Separation of variables and integral relations
for special functions, Ramanujan J.
3 1999, no. 1, 5-35, q-alg/9705006.
- Kuznetsov V.B., Sklyanin E.K., Factorisation of Macdonald polynomials,
in Symmetries and Integrability of Difference Equations (Canterbury, 1996),
London Math. Soc. Lecture Note Ser., Vol. 255,
Cambridge Univ. Press, Cambridge, 1999, 370-384, q-alg/9703013.
- Hone A.N.W., Kuznetsov V.B., Ragnisco O.,
Bäcklund transformations for many-body systems related to KdV,
J. Phys. A: Math. Gen. 32 (1999), L299-L306,
solv-int/9904003.
- Hone A.N.W., Kuznetsov V.B., Ragnisco O.,
Bäcklund transformations for the Henon-Heiles and Garnier systems,
in SIDE III - Symmetries and Integrability of Difference Equations (Sabaudia, 1998),
CRM Proc. Lecture Notes, Vol. 25, Amer. Math. Soc., Providence, RI, 2000, 231-235.
- Kuznetsov V.B., Salerno M., Sklyanin E.K.,
Quantum Bäcklund transformation for the integrable DST model, J. Phys. A: Math. Gen. 33
(2000), no. 1, 171-189, solv-int/9908002.
- Kuznetsov V.B., Nijhoff F.W. (Editors),
Kowalevski workshop on mathematical methods of regular dynamics, Papers from the workshop held at the University of Leeds (Leeds, April 12-15, 2000), J. Phys. A: Math. Gen. 34 (2001), no. 11.
- Hone A.N.W., Kuznetsov V.B., Ragnisco O.,
Bäcklund transformations for the sl(2) Gaudin magnet,
J. Phys. A: Math. Gen. 34 (2001), 2477-2490, nlin.SI/0007041.
- Kuznetsov V.B., Vanhaecke P.,
Bäcklund transformations for finite-dimensional integrable systems: a geometric approach,
J. Geom. Phys. 44 (2002), 1-40, nlin.SI/0004003.
- Adler M., Kuznetsov V.B., van Moerbeke P.,
Rational solutions to the Pfaff lattice and Jack polynomials,
Ergodic Theory Dynam. Systems 22 (2002), 1365-1405, nlin.SI/0202037.
- Kuznetsov V.B. (Editors), The Kowalevski property,
Proceedings of the Kowalevski Workshop on Mathematical Methods of Regular Dynamics (MMRD),
dedicated to the 150th anniversary of Sophie Kowalevski's birth (University of Leeds,
April 12-15, 2000), CRM Proceedings and Lecture Notes, Vol. 32,
Amer. Math. Soc., Providence, RI, 2002.
- Kuznetsov V.B.,
Kowalevski top revisited,
in The Kowalevski Property (Leeds, 2000), CRM Proc. Lecture Notes,
Vol. 32, Amer. Math. Soc., Providence, RI, 2002, 181-196, nlin.SI/0110012.
- Kuznetsov V.B.,
Simultaneous separation for the Kowalevski and Goryachev-Chaplygin gyrostats,
J. Phys. A: Math. Gen. 35 (2002), 6419-6430, nlin.SI/0201004.
- Kuznetsov V.B.,
Inverse problem for SL(2) lattices,
in SPT 2002: Symmetry and Perturbation Theory (Cala Gonone), World Sci. Publishing, River Edge,
NJ, 2002, 136-152, nlin.SI/0207025.
- Kuznetsov V.B., Mangazeev V.V., Sklyanin E.K.,
Q-operator and factorised separation chain for Jack polynomials,
Indag. Math. (N.S.) 4 (2003), 451-482, math.CA/0306242.
- Kuznetsov V.B., Petrera M.,, Ragnisco O.,
Separation of variables and Bäcklund transformations for the symmetric Lagrange top,
J. Phys. A: Math. Gen. 37 (2004), 8495-8512,
nlin.SI/0403028.
- Yuzbashyan E.A., Altshuler B.L.,
Kuznetsov V.B., Enolskii V.Z., Solution for the dynamics of the BCS and
central spin problems, J. Phys. A: Math. Gen. 38 (2005), 7831-7849,
cond-mat/0407501.
- Yuzbashyan E.A., Altshuler B.L., Kuznetsov V.B., Enolskii V.Z.,
Nonequilibrium Cooper pairing in the nonadiabatic regime, Phys. Rev. B 72 (2005), 220503(R),
4 pages, cond-mat/0505493.
- Yuzbashyan E.A., Kuznetsov V.B., Altshuler B.L.,
Integrable dynamics of coupled Fermi-Bose condensates,
Phys. Rev. B 72 (2005), 144524, 9 pages, cond-mat/0506782.
- Kuznetsov V.B., Sahi S. (Editors), Jack, Hall-Littlewood and Macdonald polynomials,
Proceedings of the Workshop held in Edinburgh (September 23-26, 2003),
Contemp. Math. 417 (2006).
- Kuznetsov V.B., Sahi S., Preface, in Jack, Hall-Littlewood and Macdonald Polynomials,
Editors V.B. Kuznetsov and S. Sahi,
Contemp. Math. 417 (2006), ix-xvii.
- Kuznetsov V.B., Sklyanin E.K.,
Factorization of symmetric polynomials, in Jack, Hall-Littlewood and Macdonald Polynomials,
Editors V.B. Kuznetsov and S. Sahi,
Contemp. Math. 417 (2006), 239-256,
math.CA/0501257.
- Kuznetsov V.B., Sklyanin E.K.,
Eigenproblem for Jacobi matrices: hypergeometric series solution,
math.CO/0509298.
- Kuznetsov V.B., Orthogonal polynomials and separation of
variables, in Orthogonal Polynomials and Special Functions, Lecture Notes
in Math., Vol. 1883, Springer, Berlin, 2006, 229-254.
- Kuznetsov V.B., Sklyanin E.K.,
Bäcklund transformation for the BC-Type Toda lattice,
SIGMA 3 (2007), 080, 17 pages,
arXiv:0707.1950.
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