Dr Georgios Papamikos
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Email
g.papamikos@essex.ac.uk -
Telephone
+44 (0) 1206 874931
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Location
2.529, Colchester Campus
Research and professional activities
Research interests
Continuous and Discrete Integrable Systems
I am interested in connections between continuous (ODEs, PDEs) and discrete (recurrence relations, lattice equations) integrable systems. These connections can be realised in one direction using Darboux transformations, or on the opposite direction using appropriate continuum limits. To this end, recently, I have been working on birational solutions of Yang-Baxter type equations and on their integrable dynamics.
Mathematical Physics
I am interested in Partial Differential Equations of mathematical physics that can be considered, in one way or another, as integrable. In particular, I am interested in their symmetry structure, conservation laws and in properties and structure of their solution space; in particular their soliton type solutions.
Algebraic methods in the study of Differential Equations
Using the theory of Lie groups and Lie algebras one can study symmetry properties of differential equations (both ordinary and partial). These properties are key ingredient for a deeper understanding of a given differential equation and can be used to simplify, find exact solutions, or even construct conservation laws associated with the differential equation at hand. These methods are algorithmic and even apply to nonlinear differential equations. At the moment I am interested in Lie symmetries of certain elliptic partial differential equations that appear in the calculus of variations and in the classification of their solutions.
Conferences and presentations
On birational and quadrirational solutions of the set theoretic Yang-Baxter equation
Invited presentation, Algebraic and Geometric Aspects of Differential and Difference Equations, Portsmouth, United Kingdom, 13/6/2024
Birational solutions of the set theoretic Yang-Baxter equation and their integrability properties
Invited presentation, Algebraic structures in the Yang-Baxter equation, Edinburgh, Edinburgh, United Kingdom, 5/6/2024
From Soliton theory to Discrete Integrable Dynamical Systems
Invited presentation, 29th School-Conference on Dynamical Systems and Complexity, National Centre For Scientific Research ”Demokritos”, Athens, Greece, 26/7/2023
Solutions of the set theoretical Yang-Baxter equation over Grassmann algebras
Invited presentation, Mathematics Days in Sofia, Sofia, Bulgaria, 13/7/2023
Solutions to Yang-Baxter type equations related to Darboux transformations
Invited presentation, ISLAND 6: Dualities and Symmetries in Integrable Systems, Isle of Skye, Scotland, 29/6/2023
Entwining Yang-Baxter maps and their extensions over Grassmann algebras
Invited presentation, 14th International Conference on Symmetries and Integrability of Difference Equations (SIDE), Warsaw, Poland, 19/6/2023
Teaching and supervision
Current teaching responsibilities
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Ordinary Differential Equations (MA202)
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Partial Differential Equations (MA323)
Publications
Journal articles (14)
Adamopoulou, P. and Papamikos, G., (2024). Entwining Yang–Baxter maps over Grassmann algebras. Physica D: Nonlinear Phenomena, 134469-134469
Adamopoulou, P., Konstantinou-Rizos, S. and Papamikos, G., (2021). Integrable extensions of the Adler map via Grassmann algebras. Theoretical and Mathematical Physics. 207 (2), 553-559
Adamopoulou, P. and Papamikos, G., (2020). Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy. Nuclear Physics B. 952, 114933-114933
Konstantinou-Rizos, S. and Papamikos, G., (2019). Entwining Yang–Baxter maps related to NLS type equations. Journal of Physics A: Mathematical and Theoretical. 52 (48), 485201-485201
Papamikos, G. and Pryer, T., (2019). A Lie symmetry analysis and explicit solutions of the two-dimensional ∞-Polylaplacian. Studies in Applied Mathematics. 142 (1), 48-64
Jackaman, J., Papamikos, G. and Pryer, T., (2019). The design of conservative finite element discretisations for the vectorial modified KdV equation. Applied Numerical Mathematics. 137, 230-251
Adamopoulou, P., Doikou, A. and Papamikos, G., (2017). Darboux–Bäcklund transformations, dressing & impurities in multi-component NLS. Nuclear Physics B. 918, 91-114
Mikhailov, AV., Papamikos, G. and Wang, JP., (2016). Dressing method for the vector sine-Gordon equation and its soliton interactions. Physica D: Nonlinear Phenomena. 325, 53-62
Mikhailov, AV., Papamikos, G. and Wang, JP., (2016). Darboux Transformation for the Vector Sine-Gordon Equation and Integrable Equations on a Sphere. Letters in Mathematical Physics. 106 (7), 973-996
Mikhailov, AV., Papamikos, G. and Wang, JP., (2014). Darboux transformation with dihedral reduction group. Journal of Mathematical Physics. 55 (11), 113507-113507
Skokos, C., Gerlach, E., Bodyfelt, JD., Papamikos, G. and Eggl, S., (2014). High order three part split symplectic integrators: Efficient techniques for the long time simulation of the disordered discrete nonlinear Schrödinger equation. Physics Letters A. 378 (26-27), 1809-1815
Papamikos, G. and Robnik, M., (2012). WKB approach applied to 1D time-dependent nonlinear Hamiltonian oscillators. Journal of Physics A: Mathematical and Theoretical. 45 (1), 015206-015206
Papamikos, G. and Robnik, M., (2011). Statistical properties of 1D time-dependent Hamiltonian systems: from the adiabatic limit to the parametrically kicked systems. Journal of Physics A: Mathematical and Theoretical. 44 (31), 315102-315102
Papamikos, GA., (2011). Lie and noether symmetries of a class of time-dependent anharmonic oscillators. Nonlinear Phenomena in Complex Systems. 14 (1), 49-59
Book chapters (1)
Adamopoulou, P. and Papamikos, G., (2021). Dressing for a Vector Modified KdV Hierarchy. In: Quantum Theory and Symmetries. Springer International Publishing. 513- 522. 9783030557768
Conferences (1)
Aldibekov, TM., Aldazharova, M., Papamikos, G. and Romanovski, VG., (2012). Integrability of a family of 3-dim polynomial systems of ODE's
Reports and Papers (3)
Adamopoulou, P. and Papamikos, G., (2023). Entwining Yang-Baxter maps over Grassmann algebras
Adamopoulou, P. and Papamikos, G., (2020). Dressing for a vector modified KdV hierarchy
Gerlach, E., Eggl, S., Skokos, C., Bodyfelt, JD. and Papamikos, G., (2013). High Order Three Part Split Symplectic Integration Schemes
Grants and funding
2020
Integrability and Analysis of PDEs (Day 1)
London Mathematical Society
