INSTITUTE FOR NUCLEAR RESEARCH AND NUCLEAR ENERGY

BULGARIAN ACADEMY OF SCIENCES

Laboratory of  "Solitons, Coherence and Geometry"

 

Prof. VLADIMIR GERDJIKOV, DSc

 

(photo)

 Vladimir Stefanov GERDJIKOV

Postal address:

 Institute for Nuclear Research and Nuclear Energy

Bulgarian Academy of Sciences

72 Tsarigradsko chaussee 

1784 Sofia

Phone: (+ 359 2) 71 44 477
Date, Place of Birth: January 07, 1947, Stara Zagora, Bulgaria 
Marital Status: Married, two children
Education:
  • B.Sc.: Graduated the Physics Department of the University of Sofia, 1964 - 1969. Master Thesis fulfilled in 1969 at Goteborg Techniska Hogskolan, Sweden, under the supervision of Prof. K.E. Eriksson. 
  • Ph.D.: 1974 - Ph.D. thesis "On the infrared singularities of the Quantum Electrodynamics" Physics Department of Leningrad State University, Leningrad, USSR. Supervized by Prof. L.D.Faddeev, Leningrad Division of Steklov Institute of Mathematics.
  • Doctor of Science: 1987 - Doctor of Science Thesis "Generating Operators of Soliton-Type Non-Linear Evolution Equations, Related to the Semi-Simple Lie Algebras", Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research, Dubna, USSR 
Professional Status:
  • 1970-71 - physicist at the Institute of Physics of the Bulgarian Academy of Sciences, Sofia, Bulgaria 
  • 1971-74 - Graduate student at Leningrad State University. 
  • 1975-76 - Research associate at INRNE, Sofia. 
  • 1977-83 - Research associate and senior research associate at the Laboratory of Theoretical Physics at the Joint Institute for Nuclear Research, Dubna. 
  • 1984-     - Research associate and senior research associate at the Institute for Nuclear Research and Nuclear Energy, Sofia.
Fields of interest:
  • Integrable nonlinear evolution equations; 
  • inhomogeneous versions of NLEE and perturbations of solitons; 
  • Soliton interactions in nonlinear optics; 
  • Hamiltonian structures of the NLEE; 
  • gauge equivalent NLEE; symmetries and conservation laws of NLEE;
  • reductions and algebraic structures of NLEE. 
Foreign languages: English, Russian
Principal publications:
  1. K. A. Edin, K. E. Eriksson, V. S. Gerdjikov, L. Matsson - Infrared end-point singularities, Physica Scripta v.2, N.6, 237-241, (1970)
  2. V. S. Gerdjikov, P. P. Kulish - On the low-energy photon theorems and the infrared divergencies, Theor. Math. Phys, v.18, n.1, 51 - 55, (1974) (In Russian); 
  3. V. S. Gerdjikov, P. P. Kulish -The low-energy structure of the Feynman S-matrix, Theor. Math. Phys. v.21, N.2, 183-194, (1974), (InRussian);
  4. V.S.Gerdjikov - The low-energy asymptotics of the Feynman amplitudes, Bulgarian J. Phys. v2, N.3, 183-193, (1975) (In Russian); 
  5. V. S. Gerdjikov, D. A. Trifonov - Normal coordinates for the non-stationary quadratic quantum systems, Compt. rendue of the Bulgarian acad. sci. v.30, N.4, 503-506, (1977) (In Russian); 
  6. V. S. Gerdjikov, P. P. Kulish - Complete integrable Hamiltonian systems related to the non-self-adjoint Dirac operator, Bulgarian J. Phys. v.5, N.4, 337-349, (1978) (In Russian); 
  7. V. S. Gerdjikov, P. P. Kulish - A method for the derivation of the Backlund transformation in the formalism of the inverse scattering method, Theor. Math. Phys. v.39, N.1, 69-74, (1979) (In Russian); 
  8. V. S. Gerdjikov, E. Kh. Khristov - On the expansions over the products of solutions of two one-dimensional Dirac systems, Matem. zametki v.28, N.4, 501-512, (1980) (In Russian); 
  9. V. S. Gerdjikov, M. I. Ivanov, P. P. Kulish - The quadratic bundle and the nonlinear equations, Theor. Math. Phys. v.44, N.3, 342-357, (1980) (In Russian); 
  10. V. S. Gerdjikov, E. Kh. Khristov - On the evolution equations solvable with the inverse scattering problem. I. The spectral theory, Bulgarian J. Phys. v.7, N.1, 28-41, (1980) (In Russian); 
  11. V. S. Gerdjikov, E. Kh. Khristov - On the evolution equations solvable with the inverse scattering problem. II. Hamiltonian structures and Backlund transformations, Bulgarian J. Phys., v.7, N.2, 119-133, (1980) (In
    Russian); 
  12. V. S. Gerdjikov, P. P. Kulish - Expansions over the "squared'' eigenfunctions of the matrix linear n n system, Sci. Notes of LOMI seminars, v.101, 46-63, (1981) (In Russian); (Translated in J. Sov. Math. v.23, N.4, 2400 - 2412 (1983)); 
  13. V. S. Gerdjikov, P. P. Kulish - The generating operator for the n n linear system, Physica D, v.3, N.3, 549-564, (1981)
  14. V. S. Gerdjikov, M. I. Ivanov, P. P. Kulish - Complete integrability of the difference evolution equations, JINR preprint E2-80-882, (1980), Dubna, USSR; 
  15. V. S. Gerdjikov, M. I. Ivanov - The block discrete Zakharov-Shabat system. I. Generalized Fourier transforms, JINR communication E2-81-811, (1981), Dubna (In English); 
  16. V. S. Gerdjikov, M. I. Ivanov - The block discrete Zakharov-Shabat system. II. The Hamiltonian structures, JINR communication E2-81-812, (1981), Dubna (In Russian); 
  17. V. S. Gerdjikov, M. I. Ivanov - The Hamiltonian structure of the difference multicomponent nonlinear Schrodinger equations, Theor. Math. Phys., v.52, N.1, 89-104, (1982) (In Russian); 
  18. V. S. Gerdjikov - On the spectral theory of the integro-differential operator L, generating nonlinear evolution equations, Lett. Math. Phys., v.6, N.6, 315-324 (1982)
  19. I. T. Gadjiev, V. S. Gerdjikov, M. I. Ivanov - Hamiltonian structures of the nonlinear evolution equations related to the polynomial bundle, Sci. Notes of LOMI seminars v.120, 55-68, (1982) (In Russian); 
  20. V. S. Gerdjikov, M. I. Ivanov - The diagonal of the resolvent and the Lax representation for the difference evolution equations, JINR communication P5-82-412, (1980), Dubna (In English);  
  21. V. S. Gerdjikov, M. I. Ivanov - The quadratic bundle of general form and the nonlinear evolution equations. I. Expansions over the "squared'' solutions are generalized Fourier transforms, Bulgarian J. Phys., v.10, N.1, 13-26, (1983) (In Russian); 
  22. V. S. Gerdjikov, M. I. Ivanov - The quadratic bundle of general form and the nonlinear evolution equations. II. Hierarchies of Hamiltonian structures, Bulgarian J. Phys., v.10, N.2, 130-143, (1983) (In Russian); 
  23. V. S. Gerdjikov, P. P. Kulish - On the multicomponent nonlinear Schrodinger equation in the case of nonzero boundary conditions, Sci. Notes of LOMI seminars v. 131, 34-46, (1983) (In Russian); (Translated in J. Sov. Math., v.30, N.4, 2261 - 2269 (1985)). 
  24. V. S. Gerdjikov, M. I. Ivanov, P. P. Kulish - Expansions over the "squared'' solutions and difference evolution equations, Journ. Math. Phys., v.25, N.1, 25-34, (1984)
  25. V. S. Gerdjikov, A. B. Yanovsky - Gauge covariant formulation of the generating operator. I. The Zakharov-Shabat system, Phys. Lett. A, v.103, N.5, 232-236, (1984)
  26. V. S. Gerdjikov, M. I. Ivanov, Y. S. Vaklev - Gauge transformations and generating operators for the discrete Zakharov-Shabat system, Inverse Problems v.2, n.4, 413-432, (1986)
  27. V. S. Gerdjikov - Gauge covariant formulation of the generalised Fourier transforms for the soliton equations, Preprint of the Inst. fur Hochenergiephysik, Berlin-Zeuthen, PHE 84-13, p.3-23, (1984)
  28. V. S. Gerdjikov, A. B. Yanovsky - Gauge covariant formulation of the generating operator. II. Systems on homogeneous spaces, Phys. Lett. A, v.110, N.2, 53-58, (1985)
  29. V. S. Gerdjikov - Generalised Fourier transforms for the soliton equations. Gauge covariant formulation, Inverse Problems v.2, N.1, 51-74, (1986)
  30. M. Boiti, V. S. Gerdjikov, F. Pempinelli - The WKIS system: Backlund transformations, generalised Fourier transforms and all that, Prog. Theor. Phys., v.75, N.5, 1111-1141, (1986)
  31. V. S. Gerdjikov, A. B. Yanovsky - The generating operator and the locality of the conserved densities for the Zakharov-Shabat system, JINR communication P5-85-505, (1985), Dubna (In Russian); 
  32. V. S. Gerdjikov - The Riemann problem, the semisimple Lie groups and the generalized Fourier transforms, In collection of papers, devoted to the 70-th anniversary of acad. Kh. Ya. Khristov, Editorial house of the Bulgarian acad. of sci., Sofia, (1988), p.145-153 (In Bulgarian); 
  33. V. S. Gerdjikov, A. B. Yanovsky - Gauge covariant theory of the generating operator. I. The Zakharov-Shabat system, Commun. Math. Phys. v.103, N.4, 549-568, (1986)
  34. V. S. Gerdjikov - Generating operators for the nolinear evolution equations of soliton type related to the semisimple Lie algebras, Autoreferat of thesis for the scientific degree "Doctor of phys. and math. sciences ", JINR 2-87-60, 1987, Dubna (In Russian); 
  35. V. S. Gerdjikov - The Zakharov-Shabat dressing method and the representation theory of the semisimple Lie algebras, Phys. Lett. A, v.126, N.3, 182-186, (1987)
  36. V. S. Gerdjikov - Completely integrable Hamiltonian systems and the classical r-matrices, In the series "Mathematical methods of the theoretical physics'', Lectures for young scientists, Editorial house of the Bulgarian acad. sci., Sofia, vol. 6, (1990) (In Bulgarian); (english version)
  37. V. S. Gerdjikov, M. I. Ivanov - Expansions over the "squared'' solutions and the inhomogeneous nonlinear Schrodinger equation, Inverse Problems, v.8, 831-847, (1992)
  38. V. S. Gerdjikov - Complete integrability, gauge equivalence and Lax representations of the inhomogeneous nonlinear evolution equations, Theor. Math. Phys., v.92, 374-386 (1992)
  39. V. S. Gerdjikov, I. M. Uzunov - Self-Frequency Shift of Dark Solitons in Optical Fibers, Phys. Rev. A, v.47, 1582-1585 (1993)
  40. V. S. Gerdjikov, A. B. Yanovski - Completeness of the eigenfunctions for the Caudrey-Beals-Coifman system, J. Math. Phys., v.35, N.7, 3687-3725 (1994)
  41. V. S. Gerdjikov - The Generalized Zakharov-Shabat System and the Soliton Perturbations, Theor. Math. Phys., v.99, N.2, 292-299 (1994)
  42. V. S. Gerdjikov, N. A. Kostov - Inverse Scattering Transform Analysis of Stokes-anti-Stokes Stimulated Raman Scattering, Phys. Rev. A, v.54, N.5, 4339-4350 (1996); (E-print: patt-sol/9502001); 
  43. I. M. Uzunov, V. S. Gerdjikov, M. Golles, F. Lederer - On the description of N-soliton interaction in optical fibers, Optics Commun., v.125, 237-242 (1996)
  44. V. S. Gerdjikov, I. M. Uzunov, E. G. Evstatiev, G. L. Diankov - Nonlinear Schrodinger Equation and N-soliton Interactions: Generalized Karpman-Soloviev Approach and the Complex Toda Chain, Phys. Rev. E, v.55, N.5, 6039-6060 (1997)
  45. V. S. Gerdjikov, G. Vilasi - The Calogero-Moser Systems and the Weyl Groups, J. Group Th. in Phys., v.3, 13-20 (1995)
  46. V. S. Gerdjikov, D. J. Kaup, I. M. Uzunov, E. G. Evstatiev - Asymptotic behavior of N-Soliton Trains of the Nonlinear Schrodinger Equation, Phys. Rev. Lett., v.77, 3943-3946, (1996)
  47. V. S. Gerdjikov, E. G. Evstatiev, D. J. Kaup, G. L. Diankov, I. M. Uzunov - Criterion and Regions of Stability for Quasi-Equidistant Soliton Trains, solv-int/9708004
  48. V. S. Gerdjikov, E. G. Evstatiev, D. J. Kaup, G. L. Diankov, I. M. Uzunov - Stability and Quasi-Equidistant Propagation of NLS Soliton Trains, Phys. Lett. A, v.241, 323-328 (1998)
  49. V. S. Gerdjikov, E. G. Evstatiev, R. I. Ivanov - The complex Toda chains and the simple Lie algebras - solutions and large time asymptotics, J. Phys. A: Math & Gen., v. 31, 8221-8232 (1998); (E-print: solv-int/9712004); 
  50. V. S. Gerdjikov, E. G. Evstatiev, R. I. Ivanov - The complex Toda Chains and the Simple Lie Algebras - Solutions and Large Time Asymptotics - II., J. Phys. A: Math & Gen., v.33, 975-1006 (2000); (E-print: solv-int/9909020);
  51. V. S. Gerdjikov, I. M. Uzunov - Adiabatic and non-adiabatic soliton interactions in nonlinear optics, Physica D152-153, 355-362 (2001)
  52. V. S. Gerdjikov, I. M. Uzunov - N-soliton train interactions and perturbed complex Toda chain in nonlinear optics: Adiabatic and non-adiabatic aspects, nlin.SI/0004031
  53. V. S.Gerdjikov, G. G. Grahovski, N. A. Kostov. Reductions of N-wave interactions related to low-rank simple Lie algebras. I: Z_2 - reductions, J. Phys. A: Math & Gen., v.34, 9425-9461 (2001); (E-print: nlin.SI/0006001); 
  54. V. S.Gerdjikov, G. G. Grahovski- Reductions and real forms of Hamiltonian systems related to N-wave type equations, nlin.SI/0009035, Balkan Physics Letters (In press); 
  55. V. S.Gerdjikov - Dynamical models of adiabatic N-soliton interactions, nlin.SI/0009036, Balkan Physics Letters (In press); 
  56. V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov, N. A. Kostov- N-wave interactions related to simple Lie algebras. Z_2- reductions and soliton solutions. Inverse Problems 17, 999-1015 (2001). (E-print: nlin.SI/0009034); 
  57. V. S. Gerdjikov. Algebraic and Analytic Aspects of Soliton Type Equations. Contemp. Math. 301 (2002), 35-68. (E-print: nlin.SI/0206014); 
  58. V. S. Gerdjikov, G. Marmo, A. Kyuldjiev, G. Vilasi. Construction of Real Forms of Complexified Hamiltonian Dynamical Systems. Europ. Phys. J. B 29, 249-254 (2002)
  59. V. S. Gerdjikov. On adiabatic N-soliton interactions and trace identities. Europ. Phys. J. B 29, 237-242 (2002)
  60. V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov. On N-wave type systems and their gauge equivalent. Europ. Phys. J. B 29, 243-248 (2002).

 

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