Dr Georgi Grahovski
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Email
gggrah@essex.ac.uk -
Location
STEM 5.37, Colchester Campus
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Academic support hours
Autumn/Spring terms 2023-24: Thursday 14:00 - 15:00 (Out of these times and out of term: by appointment).
Profile
Qualifications
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PhD Theoretical and Mathematical Physics Bulgarian Academy of Sciences, (2003)
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MSc Theoretical Physics Sofia University "St. Kliment Ohridski", Faculty of Physics, (1996)
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BSc Physics and Astronomy Sofia University "St. Kliment Ohridski", Faculty of Physics, (1995)
Appointments
ΊΪΑΟΝψ
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Lecturer in Mathematics, Mathematical Sciences, ΊΪΑΟΝψ (1/11/2013 - 30/9/2018)
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Senior Lecturer in Mathematics, Mathematical Sciences, ΊΪΑΟΝψ (1/10/2018 - present)
Research and professional activities
Research interests
Mathematical physics
Integrable systems (continuous and discrete)
Theory of solitons. Nonlinear waves
Lie groups and Lie algebras. Symmetries
Spectral theory. Analysis of PDEs
Teaching and supervision
Current teaching responsibilities
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Vector Calculus (MA210)
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Partial Differential Equations (MA323)
Previous supervision
Degree subject: Mathematics
Degree type: Master of Science (by Dissertation)
Awarded date: 9/1/2020
Degree subject: Mathematics
Degree type: Doctor of Philosophy
Awarded date: 2/7/2019
Degree subject: Mathematics
Degree type: Doctor of Philosophy
Awarded date: 25/3/2019
Publications
Publications (1)
Gerdjikov, VS. and Grahovski, GG., (2024). On affine Toda field theories related to ${\bf D}_r$ algebras and their real Hamiltonian forms
Journal articles (36)
Gerdjikov, VS. and Grahovski, GG., (2024). . International Journal of Geometric Methods in Modern Physics. 21 (10)
Gerdjikov, VS. and Grahovski, GG., (2024). . Journal of Physics: Conference Series. 2719 (1), 012004-012004
Vatansever, E., Grahovski, GG. and Fytas, NG., (2023). . European Physical Journal B: Condensed Matter and Complex Systems. 97 (3), 34-
Gerdjikov, V., Grahovski, G. and Stefanov, A., (2022). . Theoretical and Mathematical Physics. 212 (2), 1053-1072
Grahovski, GG., Mohammed, AJ. and Susanto, H., (2018). . Theoretical and Mathematical Physics. 197 (1), 1412-1429
Grahovski, GG., Mustafa, JI. and Susanto, H., (2018). . Theoretical and Mathematical Physics. 197 (1), 1430-1450
Gerdjikov, VS., Grahovski, GG. and Ivanov, RI., (2017). . Wave Motion. 71, 53-70
Gerdjikov, VS., Grahovski, GG. and Ivanov, RI., (2016). . Theoretical and Mathematical Physics. 188 (3), 1305-1321
Grahovski, GG., Konstantinou-Rizos, S. and Mikhailov, AV., (2016). . Journal of Physics A: Mathematical and Theoretical. 49 (14), 145202-145202
Grahovski, GG., Konstantinou-Rizos, S. and Mikhailov, AV., (2016). Grassmann extensions of Yang?Baxter maps. Journal of Physics A: Mathematical and Theoretical. 49 (14), creators-Grahovski=3AGeorgi_G=3A=3A
ΠΠ΅ΡΠ΄ΠΆΠΈΠΊΠΎΠ², ΠΠ‘., Gerdjikov, VS., ΠΡΠ°Ρ ΠΎΠ²ΡΠΊΠΈ, ΠΠ., Grahovski, GG., ΠΠ²Π°Π½ΠΎΠ², Π Π. and Ivanov, RI., (2016). $N$-Π²ΠΎΠ»Π½ΠΎΠ²ΡΠ΅ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Ρ $\mathcal{PT}$-ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΠ΅ΠΉ. Π’Π΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΈ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠΈΠ·ΠΈΠΊΠ°. 188 (3), 397-415
Grahovski, GG., Mikhailov, AV. and Konstantinou-Rizos, S., (2015). . Bull. Chechen State University. 17, 33-39
Grahovski, GG. and Mikhailov, AV., (2013). . Physics Letters A. 377 (45-48), 3254-3259
Grahovski, GG. and Mikhailov, AV., (2013). Integrable discretisations for a class of nonlinear SchrοΏ½dinger equations on Grassmann algebras. Physics Letters A. 377 (45-48), 3254-3259
Grahovski, GG., (2012). . Journal of Mathematical Physics. 53 (7), 073512-073512
Gerdjikov, V., Grahovski, G. and Ivanov, R., (2012). . Communications on Pure and Applied Analysis. 11 (4), 1439-1452
Gerdjikov, V., Grahovski, G. and Mikhailov, A., (2012). . Journal of Geometry and Symmetry in Physics. 25 (MARCH), 23-55
Grahovski, GG., (2012). The generalised Zakharov?Shabat system and the gauge group action. Journal of Mathematical Physics. 53 (7), creators-Grahovski=3AGeorgi_G=3A=3A
Gerdjikov, VS., Grahovski, GG., Mikhailov, AV. and Valchev, TI., (2011). . Theoretical and Mathematical Physics. 167 (3), 740-750
Gerdjikov, VS., (2011). . Symmetry, Integrability and Geometry: Methods and Applications. 7, 48-
Gerdjikov, VS., Grahovski, GG., Mikhailov, AV. and Valchev, T., (2011). Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces. Symmetry, Integrability and Geometry: Methods and Applications. 7, creators-Grahovski=3AGeorgi_G=3A=3A
ΠΠ΅ΡΠ΄ΠΆΠΈΠΊΠΎΠ², ΠΠ‘., Gerdjikov, VS., ΠΡΠ°Ρ ΠΎΠ²ΡΠΊΠΈ, ΠΠ., Grahovski, GG., ΠΡΠ°Ρ ΠΎΠ²ΡΠΊΠΈ, ΠΠ., Grahovski, GG., ΠΠΈΡ Π°ΠΉΠ»ΠΎΠ², ΠΠ., Mikhailov, AV., ΠΠ°Π»ΡΠ΅Π², Π’Π. and Valchev, TI., (2011). Π Π°ΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΠ΅ ΠΏΡΡΠΊΠΈ ΠΈ ΡΠ΅ΠΊΡΡΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΎΠΏΠ΅ΡΠ°ΡΠΎΡΡ Π΄Π»Ρ ΠΈΠ½ΡΠ΅Π³ΡΠΈΡΡΠ΅ΠΌΡΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ Π½Π° ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡΠ½ΡΡ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π°Ρ ΡΠΈΠΏΠ° A.III. Π’Π΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΈ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠΈΠ·ΠΈΠΊΠ°. 167 (3), 394-406
Gerdjikov, VS., (2010). . Symmetry, Integrability and Geometry: Methods and Applications. 6, 29-
Gerdjikov, VS. and Grahovski, GG., (2010). Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory. Symmetry, Integrability and Geometry: Methods and Applications. 6, creators-Grahovski=3AGeorgi_G=3A=3A
Grahovski, G. and Ivanov, R., (2009). . Discrete & Continuous Dynamical Systems - B. 12 (3), 579-595
Grahovski, GG. and Condon, M., (2008). . Journal of Nonlinear Mathematical Physics. 15 (supplement 3), 197-197
Atanasov, VA., Gerdjikov, VS., Grahovski, GG. and Kostov, NA., (2008). . Journal of Nonlinear Mathematical Physics. 15 (3), 291-291
Condon, M., Grahovski, GG. and Deschrijver, D., (2008). Causal and stable reduced-order model for linear high-frequency systems. Electronics Letters. 44 (14), creators-Grahovski=3AGeorgi_G=3A=3A
Grahovski, GG. and Condon, M., (2008). On the Caudrey-Beals-Coifman System and the Gauge Group Action. Journal of Nonlinear Mathematical Physics. 15 (sup3), 197-208
Condon, M., Grahovski, G. and Deschrijver, D., (2008). . Electronics Letters. 44 (14), 843-844
Gerdjikov, VS., (2006). Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras. Symmetry, Integrability and Geometry: Methods and Applications. 2, 11-
Gerdjikov, VS. and Grahovski, GG., (2005). On Reductions and Real Hamiltonian Forms of Affine Toda Field Theories. Journal of Nonlinear Mathematical Physics. 12 (Supplement 2), 155-155
ΠΠ΅ΡΠ΄ΠΆΠΈΠΊΠΎΠ², ΠΠ‘., Gerdjikov, VS., ΠΡΠ°Ρ ΠΎΠ²ΡΠΊΠΈ, ΠΠ., Grahovski, GG., ΠΠΎΡΡΠΎΠ², ΠΠ. and Kostov, NA., (2005). Π ΠΌΠ½ΠΎΠ³ΠΎΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΡΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡΡ ΡΠΈΠΏΠ° Π½Π΅Π»ΠΈΠ½Π΅ΠΉΠ½ΠΎΠ³ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ Π¨ΡΠ΅Π΄ΠΈΠ½Π³Π΅ΡΠ° Π½Π° ΡΠΈΠΌΠΌΠ΅ΡΡΠΈΡΠ½ΡΡ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π°Ρ ΠΈ ΠΈΡ ΡΠ΅Π΄ΡΠΊΡΠΈΡΡ . Π’Π΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΠΈ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠΈΠ·ΠΈΠΊΠ°. 144 (2), 313-323
Gerdjikov, VS., Grahovski, GG. and Kostov, NA., (2002). On N-wave type systems and their gauge equivalent. The European Physical Journal B - Condensed Matter. 29 (2), 243-248
Gerdjikov, VS., Grahovski, GG. and Kostov, NA., (2001). Reductions ofN-wave interactions related to low-rank simple Lie algebras: I. β€2-reductions. Journal of Physics A: Mathematical and General. 34 (44), 9425-9461
Gerdjikov, VS., Grahovski, GG., Ivanov, RI. and Kostov, NA., (2001). N -wave interactions related to simple Lie algebras. β€ 2 -reductions and soliton solutions. Inverse Problems. 17 (4), 999-1015
Books (1)
Aneva, BL., Grahovski, GG., Ivanov, RI. and Mladenov, DM., (2014). . Avangard Prima. 978--619-160-313-8
Book chapters (1)
Grahovski, GG. and Dandoloff, R., A XY Spin Chain Models on Space Curves and Analogy with Kirchhoff Rods. In: Mathematical Methods in Engineering. Springer Netherlands. 391- 401. 9781402056772
Conferences (10)
Gerdjikov, VS., Grahovski, GG., Todorov, MD. and Christov, CI., (2010). Two Soliton Interactions of BD.I Multicomponent NLS Equations and Their Gauge Equivalent
Condon, M. and Grahovski, GG., (2010). On Model Order Reduction of Perturbed Nonlinear Neural Networks with Feedback
Condon, M. and Grahovski, GG., (2009).
Condon, M. and Grahovski, GG., (2009). A parametric macromodelling technique
Condon, M. and Grahovski, GG., (2008). On Stability And Model Order Reduction Of Perturbed Nonlinear Neural Networks
Kostov, NA., Atanasov, VA., Gerdjikov, VS. and Grahovski, GG., (2007). <title>On the soliton solutions of the spinor Bose-Einstein condensate</title>
Condon, M., Grahovski, G. and Ivanov, R., (2007). Balanced Truncation Of Perturbative Representations Of Nonlinear Systems
Gerdjikov, VS., Grahovski, GG. and Kostov, NA., (2005). Multicomponent NLS-Type Equations on Symmetric Spaces and Their Reductions
Gerdjikov, VS. and Grahovski, GG., (2004). On the multi-component NLS type systems and their gauge equivalent: Examples and reductions
GRAHOVSKI, GG., (2003). ON THE REDUCTIONS AND SCATTERING DATA FOR THE GENERALIZED ZAKHAROV-SHABAT SYSTEMS
Reports and Papers (13)
Gerdjikov, VS., Grahovski, GG. and Stefanov, AA., (2022). Real Hamiltonian forms of affine Toda field theories: spectral aspects
Gerdjikov, VS. and Grahovski, GG., (2012). On the 3-wave Equations with Constant Boundary Conditions
Gerdjikov, V. and Grahovski, G., (2012). N-Wave Type Systems and their Gauge Equivalent Related to the Orthogonal Algebras
Grahovski, G., (2012). On the Reductions and Scattering Data for the CBC System
Grahovski, GG. and Gerdjikov, VS., (2012). On the Multi-Component NLS Type Equations on Symmetric Spaces: Reductions and Soliton Solutions
Gerdjikov, V. and Grahovski, G., (2012). Second Order Reductions of N-Wave Interactions Related to Low-rank Simple Lie Algebras
Gerdjikov, V. and Grahovski, G., (2012). On the Reductions and Hamiltonian Structures of N-Wave Type Equations
Grahovski, GG., Gerdjikov, VS. and Kostov, NA., (2012). New Integrable Multi-Component Nls Type Equations on Symmetric Spaces: Z4 And Z6 Reductions of Spherical Vesicles
Gerdjikov, V., Grahovski, G. and Mikhailov, A., (2012). On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on Symmetric Space
Kostov, NA., Dandoloff, R., Gerdjikov, VS. and Grahovski, GG., (2007). The Manakov system as two moving interacting curves
Dandoloff, R. and Grahovski, GG., (2006).
Grahovski, GG., Gerdjikov, VS., Kostov, NA. and Atanasov, VA., (2006).
Gerdjikov, VS. and Grahovski, GG., (2000). Reductions and real forms of Hamiltonian systems related to N-wave type equations
Grants and funding
2024
LMS Scheme 4 Research in Pairs - Collaborator visit (Dr Erol Vatansever)
London Mathematical Society
2018
Financial Support for Visits to UK
London Mathematical Society
2014
Short Visit : Dr Alexey Kostenko ( University of Vienna )
London Mathematical Society
Contact
Academic support hours:
Autumn/Spring terms 2023-24: Thursday 14:00 - 15:00 (Out of these times and out of term: by appointment).