Dr. Georgi G. Grahovski

grah-web

 

Personal Data

Position: Assistant Professor, Ph.D.
Office Address: Laboratory of Solitons, Coherence and Geometry,
Institute of Nuclear Research and Nuclear Energy,
Bulgarian Academy of Sciences,
72 Tzarigradsko Shaussee,
1784 Sofia, Bulgaria
Office Phone: (+359) 2 97-95-638
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: 13 July 1973
Birth Place: Varna, Bulgaria
Citizenship: Bulgarian

Professional Data

Education

  • BSc: 1995 Sofia University ” St. Kliment Ohridski” 
  • MSc: 1996 Sofia University ” St. Kliment Ohridski”, MSc Thesis: On the Nonlinear Schrodinger Equation with Nonvanishing Boundary Conditions (Thesis supervisor: Prof. V. S. Gerdjikov)
  • PhD: 2003 Institute for Nuclear Research and Nuclear Energy, Sofia, PhD Thesis: Reductions and hierarchy of Hamiltonian structures for the N-wave type equations ( PhD Supervisor: Prof. V. S. Gerdjikov)

Experience

  • Astronomical Observatory and Planetarium “Nicolaus Coupernicus”, Varna, Researcher: 1996 – 1998.
  • Institute for Nuclear Research and Nuclear Energy, Sofia, PhD student: 1998 – 2001.
  • Institute for Nuclear Research and Nuclear Energy, Sofia, Researcher: 2001 – 2004.
  • Dipartimento di Matematica “Federigo Enriques”, Universita degli Studi di Milano, Milano, Italy, Postdoc Researcher: March 2003 – February 2004.
  • Institute for Nuclear Research and Nuclear Energy, Sofia, Assist. Professor: 2004 – (present).
  • Laboratoire de Physique Theorique et Modelisation, Universite de Cergy-Pontoise, Cergy-Pontoise, France, Postdoc Researcher: September 2005 – August 2006.
  • School of Electronic Engineering, Dublin City University, Ireland, Postdoc Researcher: January 2007 – September 2009.
  • School of Mathematical Sciences, Dublin Institute of Technology, Ireland, Postdoc Researcher: October 2009 – December 2011.

 

Languages

  Bulgarian, English, Russian, Greek

Societies

  • Union of Bulgarian Physicists (since 1998)
  • Irish Mathematical Society (since 2009)

Interests

  • Integrable Systems (Continuous and Discrete), Soliton theory;
  • Lie groups, Lie algebras and applications to integrable systems;
  • Reductions and symmetries of integrable systems;
  • Hamiltonian systems;
  • Perturbation theory of Hamiltonian systems and their normal forms;
  • Geometry of soliton equations, Soliton curves and surfaces;
  • Applications of soliton theory to biophysical models (elastic theory of DNA, Kirchhoff rods, etc.);
  • Symmetry analysis of differential equations;
  • Nonlinear Model Reduction, Control Theory;
  • Nonlinear neural networks.

Scientific Works

Theses

 

  • MSc Thesis:On the Nonlinear Schrodinger Equation with Nonvanishing Boundary Conditions, Sofia, 1996 (In Bulgarian)
  • PhD Thesis:Reductions and hierarchy of Hamiltonian structures for the N-wave type equations, INRNE, Sofia, 2003 (In Bulgarian)

 

Book Chapters

  • M. Condon, G. G. Grahovski, Model Reduction of Weakly Nonlinear Systems, In: Advances in Electrical Engineering and Computational Science, Eds: S. I. Ao and L. Gelman, Lecture Notes in Electrical Engineering, vol. 39, Springer Verlag, Berlin - Heidelberg - New-York (2009), Chapter 2, pp. 13 – 22.

 

Papers

  • V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, Reductions of N-wave interactions related to low rank Lie algebras I: Z2 – reductions, J. Phys. A: Math. Gen. 34 (2001), 9425–9461 (E-print: nlin.SI/0006001).
  • V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov, N. A. Kostov, N-wave interactions related to simple Lie algebras. Z2- reductions and soliton solutions, Inverse Problems 17 (2001), 999–1015 (E-print: nlin.SI/0009034).
  • V. S. Gerdjikov, G. G. Grahovski, Reductions and real forms of Hamiltonian systems related to N-wave type equations, Balkan Physics Letters 9 (2000) 531–534 (E-print: nlin.SI/0009035).
  •  V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, On N-wave type systems and their gauge equivalent, European Physical Journal B 29 (2002), 243–248 (E-print: nlin.SI/0111027).
  • V. S. Gerdjikov, G. G. Grahovski, On N-wave type and NLS type systems and their gauge equivalent: generating operators and the gauge group action, Proc. of IM of NAS of Ukraine 50 (2004), 388–395.
  • V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, On the multi-component NLS type equations on symmetric spaces and their reductions, Theor. Math. Phys. 144 (2005), n.2, 1147–1156 (Russian version) .
  • V. S. Gerdjikov, G. G. Grahovski, On Reductions and Real Hamiltonian Forms of Affine Toda Field Theories, J. of Nonlin. Math. Phys. 12 (2005) Suppl. 2, 153–168 (E-print: nlin.SI/0602042).
  •  V. S. Gerdjikov, G. G. Grahovski, Real Hamiltonian Forms of Affine Toda Models, Facta Universitatis (Series: Physics, Chemistry and Technology) 4 (2006) No.2, 313–322.
  • V. S. Gerdjikov, G. G. Grahovski, Real Hamiltonian Forms of Affine Toda Field Theories Related to Exceptional Lie Algebras,  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 2 (2006), paper 022 (11 pages) (E-print: nlin.SI/0602038).
  • G. G. Grahovski, M. Condon, On the Caudrey-Beals-Coifman System and the Gauge Group Action, J. Nonlin. Math. Phys. 15 (2008), Suppl. 3, 197–208 (E-print: arXiv:0710.3302).
  • V. A. Atanasov, V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, Fordy-Kulish model and spinor Bose-Einstein condensate, J. Nonlin. Math. Phys. 15 (2008), 291–298 (E-print: arXiv:0802.4405).
  • M. Condon, G. G. Grahovski, D. Deschrijver, Causal and stable reduced-order model for linear high-frequency systems, IEEE Electronics Letters 44 (2008), No. 14, 843–844.
  • G. G. Grahovski, R. I. Ivanov, Generalised Fourier Transform and Perturbations to Soliton Equations, Discrete and Continuous Dynamical Systems B 12 (2009), no. 3, 579 – 595 (E-print: arXiv/0907.2062).
  • V. S. Gerdjikov, G. G. Grahovski, Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 6 (2010), paper 044 (29 pages) (E-print: arXiv/1006.0301).
  • V. S. Gerdjikov, G. G. Grahovski, A. V. Mikhailov, T. I. Valchev, Rational Bundles and Recursion Operators for Integrable Equations on A.III-type Symmetric Spaces, Theor. Math. Phys. 167 (2011), n.3, 740–750 (E-print: arXiv/1102.1942).
  • 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, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7 (2011), paper 096 (48 pages) (E-print: arXiv/1108.3990).
  • V. S. Gerdjikov, G. G. Grahovski, R. I. Ivanov, On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources, Comm. Pure and Applied Analysis 11 (2012), No.4, 1439–1452 (E-print: arXiv/1109.4543).
  • V. S. Gerdjikov, G. G. Grahovski, A. V. Mikhailov, T. I. Valchev, On Soliton Interactions for a Hierarchy of Generalized Heisenberg Ferromagnetic Models on SU(3)=S(U(1) x U(2)) Symmetric Space, J. of Geometry and Symmetry in Physics 25 (2012), 23 - 55 (E-print: arXiv:1201.0534).

Preprints

  • R. D. Dandoloff, G. G. Grahovski, An Exactly Solvable Case for a Thin Elastic Rod, E-print: nlin.SI/0602025.
  • R. D. Dandoloff, G. G. Grahovski, The Kirchhoff Rod as a XY Spin Chain Model, E-print: nlin.SI/0512069.
  • G. G. Grahovski, The Generalised Zakharov-Shabat System and the Gauge Group Action, E-print: arXiv/1109.5108.
  • V. S. Gerdjikov, G. G. Grahovski, On the 3-wave Equations with Constant Boundary Condition, E-print: arXiv:1204.5346

 

Published Texts Of Talks And Lectures On Conferences

  • V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, N-wave interactions related to low rank Lie algebras, In: ”Nonlinearity, integrability and all that: 20 years after NEEDS’79”,Eds: M. Boiti, L. Martina, F. Pempinelli, B. Prinari and G. Soliani, World Scientific (Singapore), 2000, pp.279–283.
  • V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, Reductions of N-wave interactions related to low rank Lie algebras, In ”Geometry, Integrability and Quantization”, Eds: Ivailo M. Mladenov and Gregory L. Naber, Coral Press, Sofia, 2000, pp.55–77 (DjVu File).
  • V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, On the reductions and Hamiltonian structures of N-wave type equations, In ”Geometry, Integrability and Quantization II”, Eds: I. Mladenov and G. Naber, Coral Press, Sofia, 2001, pp.156–170 (DjVu File).
  • V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, N-wave type systems and their gauge equivalent related to the orthogonal algebras, In ”Geometry, Integrability and Quantization III”, Eds: I. Mladenov and G. Naber, Coral Press, Sofia, 2002, pp.249–261 (DjVu File).
  • G. G. Grahovski, On The Reductions and Scattering Data for the CBC System, In ”Geometry, Integrability and Quantization III”, Eds: I. Mladenov and G. Naber, Coral Press, Sofia, 2002, pp.262–277 (DjVu File).
  • G. G. Grahovski, On the Reductions and Scattering Data for the Generalized Zakharov–Shabat Systems, In ”Nonlinear Physics: Theory and Experiment. II”, Eds: M.J.Ablowitz, M.Boiti, F.Pempinelli and B.Prinari, World Scientific, Singapore, 2003, pp.71–78.
  • V. S. Gerdjikov, G. G. Grahovski, On the multi-component NLS type systems and their gauge equivalent: Examples and reductions, In “Global Analysis and Applied Mathematics”, Eds: K. Tas, D. Krupka, O. Krupkova, D. Baleanu, AIP Conference Proceedings 729 (2004), pp.162-169.
  • G. G. Grahovski, V. S. Gerdjikov, N. A. Kostov, On the multi-component NLS type equations on symmetric spaces: Reductions and soliton solutions, In ”Geometry, Integrability and Quantization VI”, Eds: I. Mladenov and A. Hirchfeld, Softex, Sofia (2005), pp. 203-217 (DjVu File).
  • V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, On the multi-component NLS type equations on symmetric spaces: Scattering data properties and reductions, In: ”Prof. G. Manev’s Legacy in Contemporary Astronomy, Theoretical and Gravitational Physics”, Eds.V. Gerdjikov and M. Tsvetkov, Heron Press Science Series, Sofia (2006), pp. 306–317.
  • G. G. Grahovski, V. S. Gerdjikov, N. A. Kostov, V. A. Atanasov, New Integrable Multi-component NLS type Equations on Symmetric Spaces: Z4 and Z6 reductions, In ”Geometry, Integrability and Quantization VII”, Eds: I. Mladenov and M. De Leon, Softex, Sofia (2006), pp. 154–175 (E-print: nlin.SI/0603066).
  • V. A. Atanasov, V. S. Gerdjikov, G. G. Grahovski, N. A. Kostov, On the Soliton Solutions of the Multi-component NLS Equations on C:I Type Symmetric Space, In: Meetings in Physics at University of Sofia, vol. 7, A. Proykova ed., Heron Press, Sofia (2006), pp. 167–184.
  • G. Grahovski, R. D. Dandoloff, A XY Spin Chain Models on Space Curves and Analogy with Kirchhoff Rods, In: Kenan Tas et al. (eds), Mathematical Methods in Engineering, Springer Verlag, Berlin (2007), pp. 391–401.
  • N. A. Kostov; V. A. Atanasov; V. S. Gerdjikov; G. G. Grahovski, On the soliton solutions of the spinor Bose-Einstein condensate, Proc. SPIE, 6604 (2007) 66041T.
  • N. A. Kostov, R. Dandoloff, V. S. Gerdjikov, G. G. Grahovski, The Manakov system as two moving interacting curves, In: Topics in Contemporary Differential Geometry, Complex Analysis and Mathematical Physics, Eds. S. Dimiev and K. Sekigawa, World Scintific, Singapore, 2007, pp. 168 –178 (E-print: arXiv:0707.0575).
  • M. Condon, G. G. Grahovski, R. I. Ivanov, Balanced Truncation of Perturbative Representations of Nonlinear Systems, In: Proc. 21st European Conference on Modelling and Simulation, Eds: I. Zelinka, Z. Oplatkov´a, A. Orsoni, IEEE, 2007, pp. 431–434.
  • M. Condon, G. G. Grahovski,  Model reduction of a perturbative representation of a weakly nonlinear system, In: Proc. World Congress on Engineering 2008, Imperial College Press, London (2008), vols: 1–3, pp. 426-430.
  • M. Condon, G. G. Grahovski, On Stability and Model Order Reduction of Perturbed Nonlinear Neural Networks, In: Proc. 22st European Conference on Modelling and Simulation, Eds: Loucas S. Louca, Yiorgos Chrysanthou, Zuzana Oplatkov´a, Khalid Al-Begain (Editors), IEEE, 2008, pp. 475–482.
  • M. Condon, G. G. Grahovski,  A Parametric Macromodelling Technique , In: Proc. European Conference on Circuit Theory Design, Antalya (2009), IEEE, vols: 1–2, pp. 783–785.
  • G. G. Grahovski and R. I. Ivanov, The Camassa-Holm Hierarchy and Soliton Perturbations, In: BGSIAM’09 Proceedings, Eds: S. Margenov, S. Dimova and A. Slavova, Demetra Publishing, Sofia (2010), pp. 58–63 (Preprint).
  • M. Condon and G.G. Grahovski, On Model Order Reduction of Perturbed Nonlinear Neural Networks with Feedback, In: Scientific Computing in Electrical Engineering (SCEE 2008), Eds: J. Roos and L. R. J. Costa, Mathematics for Industry 14, Springer Verlag, Berlin-Heidelber-New York (2010), pp. 579–586.
  • V. S. Gerdjikov, G. G. Grahovski, Two Soliton Interactions of BD.I Multi-component NLS Equations and Their Gauge Equivalent, AIP Conference Proceedings 1301 (2010), pp.561–572 (Preprint).
  • V. S. Gerdjikov, G. G. Grahovski and R. I. Ivanov, On the (Non)-Integrability of the Perturbed KdV Hierarchy with Generic Self-consistent Sources, In: BGSIAM’10 Proceedings, Eds: S. Margenov, S. Dimova and A. Slavova, Demetra Publishing, Sofia (2011), pp.45-50 (Preprint).

Book Reviews

  • G. G. Grahovski, Book review: “The Kepler Problem: Group Theoretical Aspects, Regularization and Quantization, with Application to the Study of Perturbation”, by Bruno Cordani, Birkhauser, Basel, 2002, xvii + 439 pp. + CD included, ISBN 3-7643-6902-7, J. of Geometry and Symmetry in Physics 1 (2004), 121 - 126 (PDF File).

 

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