Dr Georgi Grahovski
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Email
gggrah@essex.ac.uk -
Telephone
+44 (0) 1206 873033
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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
University of Essex
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Lecturer in Mathematics, Mathematical Sciences, University of Essex (1/11/2013 - 30/9/2018)
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Senior Lecturer in Mathematics, Mathematical Sciences, University of Essex (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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Quantum Mechanics (MA225)
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 (33)
Gerdjikov, VS. and Grahovski, GG., (2024). On the N-waves hierarchy with constant boundary conditions. Spectral properties. International Journal of Geometric Methods in Modern Physics. 21 (10)
Gerdjikov, VS. and Grahovski, GG., (2024). On affine Toda field theories related to Dr algebras and their real Hamiltonian forms. Journal of Physics: Conference Series. 2719 (1), 012004-012004
Vatansever, E., Grahovski, GG. and Fytas, NG., (2023). Thermodynamic properties of disordered quantum spin ladders. European Physical Journal B: Condensed Matter and Complex Systems. 97 (3), 34-
Gerdjikov, V., Grahovski, G. and Stefanov, A., (2022). Real Hamiltonian forms of affine Toda field theories: spectral aspects. Theoretical and Mathematical Physics. 212 (2), 1053-1072
Grahovski, GG., Mohammed, AJ. and Susanto, H., (2018). Nonlocal Reductions of the Ablowitz–Ladik Equation. Theoretical and Mathematical Physics. 197 (1), 1412-1429
Grahovski, GG., Mustafa, JI. and Susanto, H., (2018). Nonlocal Reductions of The Multicomponent Nonlinear Schrödinger Equation on Symmetric Spaces. Theoretical and Mathematical Physics. 197 (1), 1430-1450
Gerdjikov, VS., Grahovski, GG. and Ivanov, RI., (2017). On integrable wave interactions and Lax pairs on symmetric spaces. Wave Motion. 71, 53-70
Gerdjikov, VS., Grahovski, GG. and Ivanov, RI., (2016). The N-wave equations with PT symmetry. Theoretical and Mathematical Physics. 188 (3), 1305-1321
Grahovski, GG., Konstantinou-Rizos, S. and Mikhailov, AV., (2016). Grassmann extensions of Yang–Baxter maps. 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
Grahovski, GG., Mikhailov, AV. and Konstantinou-Rizos, S., (2015). A non-commutative extension of the Adler-Yamilov Yang-Baxter map. Bull. Chechen State University. 17, 33-39
Grahovski, GG. and Mikhailov, AV., (2013). Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras. Physics Letters A. 377 (45-48), 3254-3259
Grahovski, GG. and Mikhailov, AV., (2013). Integrable discretisations for a class of nonlinear Schr�dinger equations on Grassmann algebras. Physics Letters A. 377 (45-48), 3254-3259
Grahovski, GG., (2012). The generalised Zakharov–Shabat system and the gauge group action. Journal of Mathematical Physics. 53 (7), 073512-073512
Gerdjikov, V., Grahovski, G. and Ivanov, R., (2012). On the integrability of KdV hierarchy with self-consistent sources. Communications on Pure and Applied Analysis. 11 (4), 1439-1452
Gerdjikov, V., Grahovski, G. and Mikhailov, A., (2012). On Soliton Interactions for the Hierarchy of a Generalised Heisenberg Ferromagnetic Model on Symmetric Space. 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). Rational bundles and recursion operators for integrable equations on A.III-type symmetric spaces. Theoretical and Mathematical Physics. 167 (3), 740-750
Gerdjikov, VS., (2011). Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces. 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
Gerdjikov, VS., (2010). Multi-Component NLS Models on Symmetric Spaces: Spectral Properties versus Representations Theory. 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). Generalised Fourier transform and perturbations to soliton equations. Discrete & Continuous Dynamical Systems - B. 12 (3), 579-595
Grahovski, GG. and Condon, M., (2008). On the Caudrey-Beals-Coifman System and the Gauge Group Action. Journal of Nonlinear Mathematical Physics. 15 (supplement 3), 197-197
Atanasov, VA., Gerdjikov, VS., Grahovski, GG. and Kostov, NA., (2008). Fordy-Kulish model and spinor Bose-Einstein condensate. 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). Causal and stable reduced-order model for linear high-frequency systems. 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
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. ℤ2-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. ℤ 2 -reductions and soliton solutions. Inverse Problems. 17 (4), 999-1015
Books (1)
Aneva, BL., Grahovski, GG., Ivanov, RI. and Mladenov, DM., (2014). Integrability, Recursion Operators and Soliton Interactions. Avangard Prima. 978--619-160-313-8
Conferences (9)
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). Model Reduction of Weakly Nonlinear Systems
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
Reports and Papers (6)
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
Kostov, NA., Dandoloff, R., Gerdjikov, VS. and Grahovski, GG., (2007). The Manakov system as two moving interacting curves
Dandoloff, R. and Grahovski, GG., (2006). An Exactly Solvable Case for a Thin Elastic Rod
Grahovski, GG., Gerdjikov, VS., Kostov, NA. and Atanasov, VA., (2006). New Integrable Multi-Component NLS Type Equations on Symmetric Spaces: Z_4 and Z_6 Reductions
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).