A. Refereed Journal Publications
- A. Sergyeyev, Multidimensional
integrable systems from contact geometry*, Bol. Soc.
Mat. Mex. 31 (2025), art. 26 (enhanced
arXiv version**) (open access)
- W. Kryński, A. Sergyeyev, Two-component integrable extension of
general heavenly equation*, Anal. Math. Phys. 14
(2024), art. 104, 18 pp. (open access)
- 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)
- A. Sergyeyev, Recursion
Operators for Multidimensional Integrable PDEs*, Acta
Appl. Math. 181 (2022), art.
10, 12 pp.
- 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**).
- 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)
- 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)
- 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)
- A. Sergyeyev, Integrable
(3+1)-dimensional system with an algebraic Lax pair*, Appl.
Math. Lett. 92 (2019), 196-200.
(arXiv version)
- 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)
- I. Krasil'shchik, A. Sergyeyev, Integrability of Anti-Self-Dual
Vacuum Einstein Equations with Nonzero Cosmological Constant:
An Infinite Hierarchy of Nonlocal Conservation Laws*, Ann.
Henri Poincare 20 (2019), no. 8,
2699-2715 (arXiv
version)
- A. Sergyeyev, New
integrable (3+1)-dimensional systems and contact geometry*, Lett.
Math. Phys. 108 (2018), no.
2, 359-376 (enhanced arXiv
version)
- A. Sergyeyev, Integrable
(3+1)-dimensional systems with rational Lax pairs*, Nonlinear
Dynamics 91 (2018), no. 3,
1677-1680 (arXiv
version)
- 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)
- M. Blaszak, A. Sergyeyev, Dispersionless
(3+1)-dimensional hierarchies, Proc. R. Soc. A 473 (2017),
no. 2201, art. 20160857, 16 pp. (arXiv version)
- 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)
- 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)
- 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)
- M.V. Pavlov, A. Sergyeyev, Oriented
associativity equations and symmetry consistent conjugate
curvilinear coordinate nets*, J. Geom. Phys. 85 (2014),
46-59 (arXiv version)
- O.I. Morozov, A. Sergyeyev, The
four-dimensional Martinez Alonso--Shabat equation: Reductions
and nonlocal symmetries*, J. Geom. Phys. 85 (2014),
40-45 (arXiv version)
- M. Blaszak, Z. Domanski, A. Sergyeyev, B. Szablikowski, Integrable
quantum Stackel systems, Physics Letters A 377 (2013),
2564-2572 (arXiv
version)
- 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)
- 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)
- M. Marvan, A. Sergyeyev, Recursion
operators for dispersionless integrable systems in any
dimension, Inverse Problems 28 (2012)
025011 (arXiv version)
- M. Blaszak, A. Sergyeyev, Generalized
Stackel systems, Physics Letters A 375 (2011),
2617-2623
- R.O. Popovych, A. Sergyeyev, Conservation
laws and normal forms of evolution equations, Phys.
Lett. A 374 (2010),
no.22, 2210-2217 (arXiv
version)
- 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)
- 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)
- 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, art.
404017, 15 pp. (arXiv
version)
- A. Sergyeyev, B. M. Szablikowski, Central
extensions of cotangent universal hierarchy: (2+1)-dimensional
bi-Hamiltonian systems, Phys. Lett. A 372 (2008),
7016-7023 (arXiv
version)
- A. Sergyeyev, 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)
- A. Sergyeyev, M. Blaszak, Generalized
Stackel transform and reciprocal transformations for
finite-dimensional integrable systems, J. Phys. A:
Math. Theor. 41 (2008), paper
10525 (arXiv version)
- A. Sergyeyev, Exact solvability
of superintegrable Benenti systems, J. Math. Phys. 48 (2007), no.5,
paper 052114 (arXiv
version)
- M. Blaszak, A. Sergyeyev, Natural
coordinates for a class of Benenti systems, Phys.
Lett. A 365 (2007), no.1-2,
28-33 (arXiv version)
- 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)
- A. Sergyeyev, Weakly
Nonlocal Hamiltonian Structures: Lie Derivative and
Compatibility*, SIGMA 3 (2007), paper
062 (arXiv copy) (open
access)
- A. Sergyeyev, Zero
curvature representation for a new fifth-order integrable
system*, J. Math. Sci. 151 (2008)
3227-3229 (arXiv
version)
- A. Sergyeyev, A strange
recursion operator demystified, J. Phys. A: Math.
Gen. 38 (2005), no.15,
L257-L262 (arXiv
version)
- 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)
- M. Blaszak, A. Sergyeyev, Maximal
superintegrability of Benenti systems, J. Phys. A:
Math. Gen. 38 (2005), no.1,
L1-L5 (arXiv
version)
- A. Sergyeyev, On the
classification of conditionally integrable evolution systems
in (1+1) dimensions*, J. Math. Sci. 136 (2006)
4392-4400 (arXiv
version)
- 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)
- 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)
- 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)
- A. Sergyeyev, 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)
- 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)
- 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)
- 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)
- A. Sergyeyev, Symmetries and
integrability: Bakirov system revisited, J. Phys.
A: Math. Gen. 34 (2001), no.23,
4983-4990.
- A. Sergyeyev, On
symmetries of KdV-like evolution equations, Rep.
Math. Phys. 44 (1999), no.1/2,
183-190 (arXiv
version)
- A. Sergheyev***, Generalized
symmetries of partial differential equations and quasiexact
solvability, Rep. Math. Phys. 41 (1998)
no.3, 279-286 (arXiv
version)
- 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
- 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.
- 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)
- 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.
- 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.
- 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
- 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)
- 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)
- A.G. Sergyeyev, On the class of equations for the massless
particles that are invariant under Poincare 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
- 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)
- 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).
- 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).
- 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.
- 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.
- 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