Personal Data

Occupations: Assistant Professor, Ph.D.
Office Address: Laboratory of Solitons, Coherence and Geometry,
Institute for Nuclear Research and Nuclear Energy,
Bulgarian Academy of Sciences,
72 Tzarigradsko Chaussee,
1784 Sofia, Bulgaria
Office Phone: (+359) 2 97-95-666
Office Fax: (+359) 2 975 36 19
E-mail: Този имейл адрес е защитен от спам ботове. Трябва да имате пусната JavaScript поддръжка, за да го видите.
Birth Date: February 20-th, 1979
Birth Place: Varna, Bulgaria
Citizenship: Bulgarian

Professional Data

Education

  • 2002  Bachelors Degree in Physics, Sofia University “St. Kliment Ohridski”, Bulgaria.
  • 2003  Masters Degree in Theoretical and Mathematical Physics, Sofia University “St. Kliment Ohridski”, Bulgaria.
  • 2009  Ph.D. in Theoretical and Mathematical Physics, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Bulgaria.

Experience

  • 2004 Physicist, Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences;
  • 2005 Ph.D. student, INRNE, BAS;
  • 2008 Physicist, INRNE, BAS;
  • 2009 Assistant Professor, INRNE, BAS.

Languages

English, Russian

Societies

Interests

Theory of Integrable Systems, Differential Geometry, Symmetries and Singularity Theory.

Scientific Works

Books

Thesis

  • Bachelors Thesis "Symmetries of Differential Equations. Symmetries of the Wave Equation - Conformal Group", Supervisor: Assist. Prof. Ph.D. Petko Nikolov;
  • Masters Thesis "Description of All Conformally Invariant Differential Operators, Acting on Scalar Functions", Supervisor: Assist. Prof. Ph.D. Petko Nikolov;
  • Ph.D. Thesis "Reductions of Soliton Type Nonlinear Equations on Homogeneous and Symmetric Spaces", Supervisor: Prof. D.Sc. Vladimir Gerdjikov.

Papers

  1. V. Gerdjikov, N. Kostov, T. Valchev, N-wave Equations with Orthogonal Algebras:  Z2 and Z2 x Z2 Reductions and Soliton Solutions, Sigma 3, 039,(2007), 19 pages, nlin.SI/0703002.
  2. N. Kostov, V. Gerdjikov, T. Valchev, Exact Solutions for Equations of Bose–Fermi Mixtures in One-dimensional Optical Lattice, Sigma 3, 071,(2007), 14 pages, nlin.SI/0703057.
  3. P. Nikolov, T. Valchev, Description of All Conformally Invariant Differential Operators, acting on scalar functions, JMP 48 (2007), 123516, math-ph/0410056.
  4. V. Gerdjikov, D. Kaup, N. Kostov, T. Valchev, On Classification of Soliton Solutions of Multicomponent Nonlinear Evolution Equations, J. of Physics A: Math. Theor. 41, (2008), 36 pages; e-print: V. Gerdjikov, D. Kaup, N. Kostov, T. Valchev, How many types of soliton solutions do we know?, 24 pages, Arxiv:0708.1253.
  5. V. Gerdjikov, N. Kostov, T. Valchev, Solutions of Multi-component NLS Models and Spinor Bose-Einstein Condensates, Physica D 238,n. 15, (2009), 1306-1310, nlin. PS/0802.4398.
  6. V. S. Gerdjikov, N. A. Kostov, T. I. Valchev, On Multicomponent NLS Equations with Constant Boundary Conditions, Theor. Math. Phys. 159, (2009), 786-794.
  7. V. S. Gerdjikov, A. V. Mikhailov, T. I. Valchev, Anisotropic Reductions of Integrable Equations on A.III-type Symmetric Spaces, J. of Physics A: Math. Theor. 43, (2010), 434015, Arxiv:1004.4182.
  8. V. S. Gerdjikov, A. V. Mikhailov, T. I. Valchev, Recursion Operators and Reductions of Integrable Equations on Symmetric Spaces, J. Geom. and Symm. in Phys. 20, (2010), 1-34.
  9. V. S. Gerdjikov,G. G. Grahovski, A. V. Mikhailov, T. I. Valchev, Rational Bundles and Recursion Operators for Integrable Equations on A.III Symmetric Spaces, Theor. Math. Phys. 167 (3), (2011) , 740-750.
  10. V. S. Gerdjikov,G. G. Grahovski, A. V. Mikhailov, T. I. Valchev, Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces, Sigma 7, 096 (2011), 48 pages, Arxiv:1108.3990.

Published Texts Of Talks And Lectures On Conferences

  1. P. Nikolov, T. Valchev, Description of All Conformally Invariant Differential Operators, Acting on Scalar Functions, in Proc. International Conference “Contemporary Aspects of Astronomy, Theoretical and Gravitational Physics”, May 20-22, 2004, Sofia, Eds. V. Gerdjikov and M. Tsvetkov, Heron Press 2005, 265-276.
  2. V. Gerdjikov, T. Valchev, On Soliton Solutions of N-wave Equations Associated with Symplectic Algebras, in Proc. “Meetings in Physics at University of Sofia” vol. 7, Ed. A. Proykova, Heron Press 2006, 1-7.
  3. V. Gerdjikov, T. Valchev, Breather Solutions of N-wave Equations, in Proc. 8-th International Conference on Geometry, Integrability and Quantization, June  9-14, 2006, Varna, Eds. I. Mladenov and M. de Leon,  Softex 2007, 184-200.
  4. T. Valchev, Bäcklund Transformations and Riemann-Hilbert Problem for N-wave Equations with Additional Symmetries, in Proc. 8-th International Workshop on  Complex Structures and Vector Fields, August  21-26, 2006, Sofia, Eds. S. Dimiev and K. Sekigawa, World Scientific 2007, 327-334.
  5. V. Gerdjikov, N. Kostov, T. Valchev, Soliton Equations with Deep Reductions. Generalized Fourier Transforms, in Proc. 8-th International Workshop on Complex Structures and Vector Fields, August 21-26, 2006, Sofia, Eds. S. Dimiev and K. Sekigawa, World Scientific 2007, 85-96.
  6. T. Valchev, On the Kaup-Kupershmidt Equation. Completeness of the Squared Solutions, in Proc. 9-th International Conference on Geometry, Integrability and Quantization, June 8-13, 2007, Varna, Eds. I. Mladenov and M. de Leon, Softex 2008, 12 pages.
  7. N. Kostov, V. Gerdjikovand T. Valchev,Bose-Fermi Mixtures in Two Optical Lattices, in Proc. 9-th International Conference on Geometry, Integrability and Quantization, June 8-13, 2007, Varna, Eds. I. Mladenov and M. de Leon, Softex 2008, 224-240.
  8. T. Valchev, New Integrable Equations of mKdV Type, in Proc. 9-th International Workshop on Complex Structures, Integrability and Vector Fields, August 25-29, 2008, Sofia, Eds. S. Dimiev and K. Sekigawa, 10 pages;
  9. T. Valchev, On Generalized Fourier Transform for Kaup-Kupershmidt Type Equations, in Proc.  10-th International Conference on Geometry, Integrability and Quantization, June 5-10, 2009, Varna, Eds. I. Mladenov and M. de Leon, Avangard Prima 2010, 13 pages.
  10. T. Valchev, On Certain Reductions of Integrable Equations on Symmetric spaces, in Proc. 10-th Int. Workshop on Complex structures, Integrability and Vector Fields, September 13-17, 2010, Sofia, Eds: K. Sekigawa, V. Gerdjikov, Y. Matsushita and I. Mladenov, 154-164, AIP Conference Proceedings, Melville, New-York, 2011.

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