Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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.

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Dr. Vadim B. Kuznetsov: List of publications

  1. 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).
  2. 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).
  3. 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.
  4. 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.
  5. 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).
  6. 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.
  7. Kuznetsov V.B., Generalized polyspheroidal periodic functions and the quantum inverse scattering method, J. Math. Phys. 31 (1990), 1167-1174.
  8. Komarov I.V., Kuznetsov V.B., Quantum Euler-Manakov top on the 3-sphere S3, J. Phys. A: Math. Gen. 24 (1991), L737-L742.
  9. 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).
  10. 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).
  11. 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.
  12. 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).
  13. Kuznetsov V.B., Equivalence of two graphical calculi, J. Phys. A: Math. Gen. 25 (1992), 6005-6026.
  14. 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.
  15. 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.
  16. Christiansen P.L., Jørgensen M.F., Kuznetsov V.B., On integrable systems close to the Toda lattice, Lett. Math. Phys. 29 (1993), 165-173.
  17. 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).
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. Kuznetsov V.B., Sklyanin E.K., Separation of variables in A2 type Jack polynomials, RIMS Kokyuroku 919 (1995), 27-43, solv-int/9508002.
  25. 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.
  26. 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.
  27. Kuznetsov V.B., Hidden symmetry of the quantum Calogero-Moser system, Phys. Lett. A 218 (1996), 212-222, solv-int/9509001.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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.
  41. 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.
  42. 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.
  43. 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.
  44. Kuznetsov V.B., Simultaneous separation for the Kowalevski and Goryachev-Chaplygin gyrostats, J. Phys. A: Math. Gen. 35 (2002), 6419-6430, nlin.SI/0201004.
  45. 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.
  46. 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.
  47. 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.
  48. 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.
  49. 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.
  50. 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.
  51. 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).
  52. 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.
  53. 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.
  54. Kuznetsov V.B., Sklyanin E.K., Eigenproblem for Jacobi matrices: hypergeometric series solution, math.CO/0509298.
  55. 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.
  56. 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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