Publications

A. Refereed Journal Publications

  1. A. Sergyeyev, Multidimensional integrable systems from contact geometry*, Bol. Soc. Mat. Mex. 31 (2025), art. 26, 14 pp. (enhanced arXiv version**) (open access)
  2. W. Kryński, A. Sergyeyev, Two-component integrable extension of general heavenly equation*, Anal. Math. Phys. 14 (2024), art. 104, 18 pp. (open access)
  3. A. Sergyeyev, Complete Description of Local Conservation Laws for Generalized Dissipative Westervelt Equation*, Qual. Theor. Dyn. Sys. 23 (2024), art. 209, 8 pp. (open access)
  4. A. Sergyeyev, Recursion Operators for Multidimensional Integrable PDEs*, Acta Appl. Math. 181 (2022), art. 10, 12 pp.
  5. M. Blaszak, K. Marciniak, A. Sergyeyev, Deforming Lie algebras to Frobenius integrable nonautonomous Hamiltonian systems, Rep. Math. Phys. 87 (2021), no. 2, 249-263 (arXiv version).
  6. A. Sergyeyev, A. Wojnar, The Palatini star: exact solutions of the modified Lane–Emden equation, Eur. Phys. J. C 80 (2020), art. 313 (open access via SCOAP3)
  7. S. Opanasenko, A. Bihlo, R.O. Popovych, A. Sergyeyev, Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model, Physica D 402 (2020), art. 132546 (arXiv version)
  8. S. Opanasenko, A. Bihlo, R.O. Popovych, A. Sergyeyev, Extended symmetry analysis of isothermal no-slip drift flux model, Physica D 402 (2020), art. 132188 (arXiv version)
  9. A. Sergyeyev, Integrable (3+1)-dimensional system with an algebraic Lax pair, Appl. Math. Lett. 92 (2019), 196–200. (arXiv version)
  10. A. Sergyeyev, S. Skurativskyi, V. Vladimirov, Compacton solutions and (non)integrability of nonlinear evolutionary PDEs associated with a chain of prestressed granules, Nonlinear Analysis: Real World Appl. 47 (2019), 68–84 (arXiv version)
  11. I. Krasil'shchik and A. Sergyeyev, Integrability of Anti-Self-Dual Vacuum Einstein Equations with Nonzero Cosmological Constant: An Infinite Hierarchy of Nonlocal Conservation Laws*, Ann. Henri Poincaré 20 (2019), no. 8, 2699–2715 (arXiv version)
  12. A. Sergyeyev, New integrable (3+1)-dimensional systems and contact geometry*, Lett. Math. Phys. 108 (2018), no. 2, 359-376 (arXiv version has some typos fixed)
  13. A. Sergyeyev, Integrable (3+1)-dimensional systems with rational Lax pairs*, Nonlinear Dynamics 91 (2018), no. 3, 1677-1680 (arXiv version)
  14. A. Sergyeyev, A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems*, J. Math. Analysis and Appl. 454 (2017), no. 2, 468-480 (arXiv version)
  15. M. Blaszak, A. Sergyeyev, Dispersionless (3+1)-dimensional hierarchies, Proc. R. Soc. A 473 (2017), no. 2201, art. 20160857, 16 pp. (arXiv version)
  16. A. Sergyeyev, R. Vitolo, Symmetries and conservation laws for the Karczewska--Rozmej--Rutkowski--Infeld equation, Nonlinear Analysis: Real World Applications 32 (2016), 1-9 (arXiv version)
  17. I.S. Krasil'shchik, A. Sergyeyev, O.I. Morozov, Infinitely many nonlocal conservation laws for the ABC equation with A+B+C<>0*, Calc. Var. PDEs 55 (2016), article 123 (arXiv version)
  18. I.S. Krasil'shchik, A. Sergyeyev, Integrability of S-deformable surfaces: Conservation laws, Hamiltonian structures and more J. Geom. Phys. 97 (2015), 266-278 (arXiv version)
  19. M.V. Pavlov, A. Sergyeyev, Oriented associativity equations and symmetry consistent conjugate curvilinear coordinate nets, J. Geom. Phys. 85 (2014), 46-59 (arXiv version)
  20. O.I. Morozov, A. Sergyeyev, The four-dimensional Martínez Alonso–Shabat equation: Reductions and nonlocal symmetries, J. Geom. Phys. 85 (2014), 40-45 (arXiv version)
  21. M. Blaszak, Z. Domanski, A. Sergyeyev, B. Szablikowski, Integrable quantum Stäckel systems, Physics Letters A 377 (2013), 2564-2572 (arXiv version)
  22. G.I. Burde, A. Sergyeyev, Ordering of two small parameters in the shallow water wave problem, J. Phys. A: Math. Theor. 46 (2013), 075501, included into J Phys A Highlights Collection of 2013 (arXiv version)
  23. A. Sergyeyev, Coupling constant metamorphosis as an integrability-preserving transformation for general finite-dimensional dynamical systems and ODEs, Physics Letters A 376 (2012), no.28-29, 2015-2022  (arXiv version)
  24. M. Marvan and A. Sergyeyev, Recursion operators for dispersionless integrable systems in any dimension, Inverse Problems 28 (2012) 025011 (arXiv version)
  25. M. Blaszak and A. Sergyeyev, Generalized Stäckel systems, Physics Letters A 375 (2011), 2617-2623
  26. R.O. Popovych and A. Sergyeyev, Conservation laws and normal forms of evolution equations, Phys. Lett. A 374 (2010), no.22, 2210-2217 (arXiv version)
  27. A. Sergyeyev, Infinitely Many Local Higher Symmetries without Recursion Operator or Master Symmetry: Integrability of the Foursov–Burgers System Revisited*, Acta Applicandae Mathematicae 109 (2010), no.1, 273-281 (arXiv version)
  28. M. Blaszak, A. Sergyeyev, A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems, Rep. Math. Phys. 64  (2009), no.1–2, 341-354 (arXiv version)
  29. A. Sergyeyev, Infinite hierarchies of nonlocal symmetries of the Chen-Kontsevich-Schwarz type for the oriented associativity equations. J. Phys. A: Math. Theor. 42 (2009), no. 40, 404017, 15 pp. (arXiv version)
  30. A. Sergyeyev and B. M. Szablikowski, Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems, Phys. Lett. A 372 (2008), 7016-7023 (arXiv version)
  31. A. Sergyeyev and P. Krtouš, Complete set of commuting symmetry operators for the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetimes*, Phys. Rev. D 77 (2008), paper 044033 (arXiv version) 
  32. A. Sergyeyev and M. Blaszak, Generalized Stäckel transform and reciprocal transformations for finite-dimensional integrable systems, J. Phys. A: Math. Theor. 41 (2008), paper 10525 (arXiv version)
  33. A. Sergyeyev, Exact solvability of superintegrable Benenti systems, J. Math. Phys. 48 (2007), no.5, paper 052114 (arXiv version)
  34. M. Blaszak, A. Sergyeyev, Natural coordinates for a class of Benenti systems, Phys. Lett. A 365 (2007), no.1-2, 28-33 (arXiv version)
  35. A. Sergyeyev, D. Demskoi, Sasa-Satsuma (complex modified Korteweg—de Vries II) and the complex sine-Gordon II equation revisited: Recursion operators, nonlocal symmetries, and more, J. Math. Phys. 48 (2007), no.4, paper 042702 (arXiv version)
  36. A. Sergyeyev, Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility, SIGMA 3 (2007),  paper 062 (arXiv copy) (open access)
  37. A. Sergyeyev, Zero curvature representation for a new fifth-order integrable system*, J. Math. Sci. 151 (2008) 3227-3229 (in Russian: Fund. Prikl. Mat. 12 (2006), no.7, 227-229) (arXiv version) 
  38. A. Sergyeyev, A strange recursion operator demystified, J. Phys. A: Math. Gen. 38 (2005), no.15, L257-L262 (arXiv version) 
  39. A. Sergyeyev, Why nonlocal recursion operators produce local symmetries: new results and applications, J. Phys. A: Math. Gen. 38 (2005), no.15, 3397-3407 (arXiv version) 
  40. M. Blaszak, A. Sergyeyev, Maximal superintegrability of Benenti systems, J. Phys. A: Math. Gen. 38 (2005), no.1, L1-L5 (arXiv version) 
  41. A. Sergyeyev, On the classification of conditionally integrable evolution systems in (1+1) dimensions*, J. Math. Sci. 136 (2006) 4392-4400 (in Russian: Fund. Prikl. Mat. 10 (2004), no. 1, 243-253) (arXiv version) 
  42. A. Sergyeyev, A simple way of making a Hamiltonian system into a bi-Hamiltonian one*, Acta Appl. Math. 83 (2004), no.1-2, 183-197 (arXiv version) 
  43. A. Sergyeyev, Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: a new application for formal symmetries*, Acta Appl. Math.83 (2004), no.1-2, 95-109 (arXiv version) 
  44. M. Marvan, A. Sergyeyev, Recursion operator for the stationary Nizhnik--Veselov--Novikov equation, J. Phys. A: Math. Gen. 36 (2003), no.5, L87-L92 (arXiv version) 
  45. A. Sergyeyev and J.A. Sanders, A remark on nonlocal symmetries for the Calogero--Degasperis--Ibragimov--Shabat equation, J. Nonlin. Math. Phys. 10 (2003), no. 1, 78-85 (arXiv copy) 
  46. A. Sergyeyev, On sufficient conditions of locality for hierarchies of symmetries of evolution systems, Rep. Math. Phys. 50 (2002), no.3, 307-314 Preprint version (gzipped PostScript) 
  47. A. Sergyeyev, Constructing conditionally integrable evolution systems in (1+1) dimensions: a generalization of invariant modules approach, J. Phys. A: Math. Gen. 35 (2002), 7653-7660 Preprint version (gzipped PostScript)
  48. A. Sergyeyev, On homogeneous symmetries for evolution systems with constraints, Rendiconti del Circolo Matematico di Palermo, 2002, Serie II, No. 69, 219-231. Preprint version (gzipped PostScript)
  49. A. Sergyeyev, Symmetries and integrability: Bakirov system revisited, J. Phys. A: Math. Gen. 34 (2001), no.23, 4983-4990.
  50. A. Sergyeyev, On symmetries of KdV-like evolution equations, Rep. Math. Phys. 44 (1999), no.1/2, 183-190 (arXiv version) 
  51. A. Sergheyev***, Generalized symmetries of partial differential equations and quasiexact solvability, Rep. Math. Phys. 41 (1998) no.3, 279-286
    (arXiv version) 
  52. A.G. Sergheyev***, A relativistic Coulomb problem for the modified Stueckelberg equation, Ukr. J. Phys. 42 (1997), no.10, 1171-1174 Preprint version

B. Articles in Refereed Proceedings

  1. A. Sergyeyev, The structure of cosymmetries and a simple proof of locality for hierarchies of symmetries of odd order evolution systems, Proc. Fifth Int. Conf. ``Symmetry in Nonlinear Mathematical Physics", published in Proceedings of Institute of Mathematics of NAS of Ukraine, 2004, 50, Part 1, p.238-245.
  2. A. Sergyeyev, On a class of inhomogeneous extensions for integrable evolution systems, Proc. 8th Int. Conf. on Diff.Geom. and its Appl., 2001, p.243-252 (arXiv version)
  3. A. Sergyeyev and J.A. Sanders, The Complete Set of Generalized Symmetries for the Calogero--Degasperis--Ibragimov--Shabat Equation, Proc. 4th Int. Conf. "Symmetry in Nonlinear Mathematical Physics", published in Proceedings of Institute of Mathematics of NAS of Ukraine, 2002, 43, Part 1, p.209-214.
  4. A. Sergyeyev, On local time-dependent symmetries of integrable evolution equations, Proc. 3rd Int. Conference "Symmetry in Nonlinear Mathematical Physics" (Kyiv, July 13-18, 1999), published in Proceedings of Institute of Mathematics of NAS of Ukraine, 2000, 30, Part 1, p.196-203. 
  5. A. Sergyeyev, Nonlocal symmetries and formal symmetries for evolution equations, Group and Analytic Methods in Mathematical Physics, Proceedings of Institute of Mathematics of NAS of Ukraine, 2001, 35, p.227-236 
  6. A. Sergyeyev, On recursion operators and nonlocal symmetries of evolution equations, Proc. Sem. Diff. Geom., D. Krupka ed., Mathematical Publications, Silesian University in Opava, Opava, Czech Republic, 2000, 2, p.159-173 (arXiv version)
  7. A. Sergyeyev, On time-dependent symmetries and formal symmetries of evolution equations, in Symmetry and Perturbation Theory, A. Degasperis and G. Gaeta eds., Singapore, World Scientific, 1999, p.303-308. (arXiv version) 
  8. A.G. Sergyeyev, On the class of equations for the massless particles that are invariant under Poincaré parasupergroup, in Proc. 2nd All-Ukrainian Conference of young scientists (Kyiv, 16-18 May 1995), Kyiv, 1995, p.41-46 (in Ukrainian).

C. Other Works

  1. A. Sergyeyev, Time dependence and (non)commutativity of symmetries of evolution equations, in "Noncommutative Structures in Mathematics in Physics" (Proc. NATO ARW), S. Duplij and J. Wess eds., Kluwer, 2001, p.379-390. (arXiv version)
  2. A.G. Sergyeyev, Higher Symmetries and Parasupersymmetries of Evolution Equations, Ph.D. thesis, Kyiv, Institute of Mathematics of NAS of Ukraine, 2000, 130 p. (in Ukrainian).
  3. A.G. Sergyeyev, On the structure of generalized symmetries for nonlinear evolution equations, Visnyk Kyivs'kogo Universytetu (Bulletin of the University of Kiev), Series: Physical and mathematical Sciences, 1999, no.3, p.61-70 (in Ukrainian).
  4. A.G. Sergheyev***, On time-dependent symmetries of evolution equations, Symmetry and Analytic Methods in Mathematical Physics, Proceedings of Institute of Mathematics of NAS of Ukraine, 1998, 19, p. 216-220.
  5. A.G. Sergeyev***, On parasupersymmetries in a relativistic Coulomb problem for the modified Stueckelberg equation, in Proc. 2nd Int. Conference "Symmetry in Nonlinear Mathematical Physics" (Kyiv, July 7-13, 1997), Kyiv, 1997, 2, p.331-335.
  6. O.F. Kalaida, A.G. Sergyeyev, O.V. Galkin, New variant of matrix algorithms of numerical integration for regular, weakly singular, and singular integrals, Visnyk Kyivs'kogo Universytetu (Bulletin of the University of Kiev), Series: Physical and Mathematical Sciences, 1993, no.3, p.18-22 (in Ukrainian).
*Full text at the link is free to read even without valid subscription 

**arXiv version means a preprint full-text version available free of charge from arXiv.org

***Sergheyev = Sergeyev = Sergyeyev

Back to my main page