Fedorchuk Vasyl Maksymovych
Education:
postgraduate study
at the
Scientific title: senior researcher
(1990)
Scientific degree: Doctor of Sciences
(1999)
Position: Leading Research Fellow
Research interests: finite-dimensional
Lie algebras, differential equations with non-trivial symmetry groups,
application of the local Lie groups of point transformations in theoretical and
mathematical physics
Field
of scientific research: study of structural properties of the
finite-dimensional Lie algebras and application of the results obtained for
construction and investigation of classes of differential equations invariant
with respect to these Lie algebras
Main scientific
results:
1.
Description of all nonconjugate subalgebras of
the Lie algebra of the Poincaré group P(1,4). The conjugation was considered under the group
P(1,4). (With W.I. Fushchych, A.F. Barannyk,
L.F.
Barannyk).
2.
Construction of functional bases of invariants
for all nonconjugate subalgebras of the Lie algebra of the group P(1,4).
3.
Symmetry reduction and construction classes of
exact solutions for the following differential equations:
– eikonal equation.
(With I.M. Fedorchuk);
–
Euler-Lagrange-Born-Infeld equation. (With I.M. Fedorchuk) ;
– homogeneous and
inhomogeneous Monge-Ampère equation.
(With O.S. Leibov);
– linear and
nonlinear five-dimensional wave equation;
– five-dimensional Dirac equation.
(With
I.M. Fedorchuk and V.I. Fedorchuk).
4. Equivalence criteria for
arbitrary two functional bases of differential invariants of arbitrary finite
order of nonconjugate subalgebras of Lie algebras of local Lie groups of point
transformations. (With V.I. Fedorchuk).
5. Construction of non-equivalent functional bases of first-order
differential invariants for all nonconjugate subalgebras of the Lie algebra of
the group P(1,4). (With V.I. Fedorchuk).
6. Classification of all
nonconjugate subalgebras (dimL ≤ 5) of the Lie algebra of the group P(1,4) in classes of isomorphic subalgebras. (With V.I. Fedorchuk).
7. Construction of invariant operators (generalized Casimir operators) for all nonconjugate subalgebras (dimL ≤ 5) of the Lie algebra
of the group P(1,4). (With V.I. Fedorchuk).
8. Classification of symmetry
reductions for the eikonal equation. (With V.I. Fedorchuk).
9. Classification of symmetry reductions for
the Euler-Lagrange-Born-Infeld equation. (With V.I. Fedorchuk).
10. Classification of symmetry reductions and
invariant solutions for the (1+3)-dimensional homogeneous and inhomogeneous
Monge-Ampère equati-ons. (With V.I.
Fedorchuk).
Major publications:
Monographies
Vasyl Fedorchuk, Volodymyr Fedorchuk. Classification of Symmetry
Reductions for the Eikonal Equation. - Lviv: Pidstryhach Institute for Applied
Problems of Mechanics and Mathematics of
Papers:
1.
Fedorchuk V.M. Splitting subalgebras of the Lie algebra of the
generalized Poincaré group P(1,4) . (Russian) // Ukrain. Mat. Zh. – 1979. – 31, N 6. – P. 717–722. English
translation: Ukrainian Math. J., 31 (1979), no. 6, 554–558 (1980).
2.
Fedorchuk
V.M. Nonsplitting subalgebras of the Lie algebra of the generalized
Poincaré group P(1,4). (Russian)
// Ukrain. Mat. Zh. - 1981. - 33, N 5. P. 696-700. English
translation: Ukrainian Math. J. 33 (1981), no. 5, 535-538 (1982).
3.
Fushchich
W.I., Barannik A.F., Barannik L.F. and Fedorchuk V.M. Continuous subgroups of the
Poincaré group P(1,4) //
J. Phys. A: Math. Gen. – 1985. – 18, N 14. – P. 2893–2899.
4.
Fedorchuk V.M., Fedorchuk I.M. and Leibov O.S. Reduction
of the Born-Infeld, the Monge-Ampère and the eikonal equation to linear
equations. (Russian) // Dokl. Akad. Nauk Ukrainy. – 1991,
N 11. – P. 24–26.
5.
Fedorchuk
V. Symmetry Reduction and Exact Solutions of the Euler-Lagrange-Born-Infeld, the Multidimensional Monge–Ampère and the Eikonal Equations // J. Nonlinear Math.
Phys. – 1995.– v. 2, N 3–4. – P. 329–333.
6.
Fedorchuk V.M. Symmetry reduction and some exact solutions of a
nonlinear five-dimensional wave equation. (Ukrainian) // Ukrain. Mat. Zh. – 1996. – 48,
N 4. – P. 574–577; translation in Ukrainian Math. J., 48 (1996), no. 4, 636–640 (1997).
7.
Fedorchuk V.M., Fedorchuk
I.M. and Fedorchuk V.I. Symmetry
reduction of the five-dimensional Dirac equation. (Ukrainian)
// Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, 1999, N 9, P. 24–29.
8. Fedorchuk V.M. Invariants of subgroups of the generalized
Poincaré group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2000. - 43, N 2. - P. 64-69.
9.
Fedorchuk V.M. and
Fedorchuk V.I. Differential invariants of the first order of splitting subgroups of the
generalized Poincaré
group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2001.- 44,
N 1. - P. 16-21.
10. Fedorchuk V.M. and
Fedorchuk V.I. On first-order differential invariants for splitting subgroups
of the generalized Poincaré group P(1,4). (Ukrainian) // Dopov. Nats.
Akad. Nauk Ukr. – 2002, N 5. – P. 36–42.
11. Fedorchuk V, On invariants of continuous
subgroups of the generalized Poincaré group P(1,4) // Universitatis
Iagellonicae Acta Mathematica, Fasciculus XL, 2002, 197-205.
12. Fedorchuk V.M. and Fedorchuk V.I, On new
differential equations of the first order in the space M(1,4)× R(u) with
non-trivial symmetries // Annales Academiae Paedagogicae Cracoviensis, Studia
Mathematica III (2003), Folia 16, 49-53.
13. Vasyl Fedorchuk and Volodymyr Fedorchuk, On
the Differential First - Order Invariants of the Non-Splitting Subgroups of the
Poincaré group P(1,4) // Proceedings of Institute of Mathematics of NAS
of Ukraine, 2004, 50, Part 1, 85-91.
14. Vasyl M. Fedorchuk and Volodymyr I. Fedorchuk,
On the differential first-order invariants for the non-splitting subgroups of
the generalized Poincaré group P(1,4) // Annales Academiae Paedagogicae
Cracoviensis, Studia Mathematica IV (2004), Folia 23, 65-74.
15. Fedorchuk V.M. and
Fedorchuk V.I. On functional bases of first-order differential invariants of
continuous subgroups of the Poincaré group P(1,4). (Ukrainian) // Mat.
Metodi Fiz.-Mekh. Polya. - 2005. - 48, N 4. - P. 51-58.
16. Fedorchuk V.M. and Fedorchuk V.I., First-order
differential invariants of the splitting subgroups of the Poincaré group
P(1,4) // Universitatis Iagellonicae Acta Mathematica, 2006, Fasciculus XLIV,
35-44.
17. Fedorchuk V.M. and Fedorchuk V.I. On
classification of low-dimensional nonconjugate subalgebras of the Lie algebra
of the Poincaré group P(1,4). (Ukrainian) // Proceedings of the
18. Fedorchuk V.M. and
Fedorchuk V.I. On invariant operators of low-dimension nonconjugate subalgebras
of the Lie algebra of the Poincaré group P(1,4). (Ukrainian) // Mat.
Metodi Fiz.-Mekh. Polya. - 2007. - 50, N 1. - P. 16-23.
19.
Fedorchuk V.M. and Fedorchuk V.I., On functional bases of
the first-order differential invariants for nonconjugate subgroups of the Poincaré group P(1,4) // Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica VII (2008), 41–50.
20. Fedorchuk V.M. and
Fedorchuk V.I. On the equivalence of functional bases of differential
invariants of nonconjugate subgroups of local Lie groups of point
transformations. (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. – 2009. - 52, ¹ 2. – P. 23-27 ;
translation in J. Math. Sci., 170 (2010), no. 5, 588–593.
21.
Fedorchuk V. M. and Fedorchuk V.I. Invariant
operators for four-dimensional nonconjugate subalgebras of the Lie algebra of
the Poincaré group P(1,4). (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. - 2010. - 53, N 4. - P. 17-27; translation in J. Math.
Sci., 181 (2012), no. 3, 305–319.
22. Vasyl
Fedorchuk and Volodymyr Fedorchuk,
Invariant Operators of Five-Dimensional Nonconjugate Subalgebras of the Lie
Algebra of the Poincaré Group P(1,4) // Abstract and Applied Analysis, vol. 2013, Article ID
560178, 16 pages, 2013. doi:10.1155/2013/560178.
23. Vasyl
Fedorchuk and Volodymyr Fedorchuk, On
Classification of Symmetry Reductions for the Eikonal Equation // Symmetry 2016,
8(6), 51; 32pages, doi:10.3390/sym8060051.
24. Fedorchuk V. and Fedorchuk V. On classification of
symmetry reductions for partial differential equations // Collection of the
works dedicated to 80th of anniversary of B.J. Ptashnyk, 241-255, Pidstryhach
Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine,
Lviv, 2017.
25. Fedorchuk V.M., Fedorchuk V.I., On symmetry reduction of
the Euler–Lagrange–Born–Infeld equation to linear ODEs, in Symmetry and
Integ-rability of Equations of Mathematical Physics, Collection of Works of
Institute of Mathematics, Kyiv 16 (2019), no. 1, 193-202.
26. V.M. Fedorchuk, V.I. Fedorchuk, On the classification of
symmetry re-duction and invariant solutions for the Euler-Lagrange-Born-Infeld
equation. Ukr. J. Phys. 2019. Vol. 64, No. 12, 1103-1107, https://doi.org/10.15407/ujpe64.12.1103
27. Fedorchuk V.M. and Fedorchuk V.I. On
Symmetry Reduction of the (1 + 3)-Dimensional Inhomogeneous Monge-Ampère
Equation to the First-Order ODEs // Applied Mathematics, 2020, 11, 1178–1195. https://doi.org/10.4236/am.2020.1111080.
28. Fedorchuk V.M., Fedorchuk V.I. On the
classification of symmetry reductions for the (1+3)-dimensional monge –
ampère equation // Mat. Metody Fiz.-Mekh. Polya. 63, (2), 7–16, (2020).
(in Ukrainian)
29. Vasyl Fedorchuk, Volodymyr
Fedorchuk. On symmetry reduction and some classes of invariant solutions of the
(1 + 3)-dimensional homogeneous Monge-Ampère equation. // Proceedings of
the
30.
Fedorchuk V.M., Fedorchuk V.I. On
reduction of the (1+3)-dimensional inhomogeneous Monge-Ampère equation
to the first-order partial differential equations // Ukr. Math. J. – 2022. – 74,
No. 3. – P.
418–426. – https://doi:10.37863/umzh.v74i3.6996. (in Ukrainian)
Conference
proceedings:
16. Fedorchuk Vasyl, Fedorchuk Volodymyr, Classification of reduced
equations for the eikonal equation // Symmetry and Integrability of Equations
of Mathematical Physics, International workshop in honor of Wilhelm Fushchych
(December 17-20, 2016, Kyiv,
21. Vasyl Fedorchuk. On Symmetry Reduction of Some Partial
Differential Equations. Modern problems
of Mechanics and Mathematics: collection of scientific papers in 3 vol. /
Edited by A.Ì. Samoilenko, R.M. Kushnir
[Electronic resource] // Pidstryhach Institute for Applied Problems of
Mechanics and Mathematics NAS of Ukraine. – 2018. – Vol. 3. – p. 187., http://www.iapmm.lviv.ua/mpmm2018/Volume
3.pdf.
22. Fedorchuk
Vasyl. On symmetry reduction and invariant solutions of some
partial differential equations. The 32nd International Colloquium on Group
Theoretical Methods in Physics (Group32) (9-13 July 2018, Czech Technical
University in Prague, Czech Republic). Book of Abstracts. - p. 23., http://kmlinux.fjfi.cvut.cz/~burdices/Group32/new-booklet.pdf.
27.
V.
M. Fedorchuk, V. I. Fedorchuk On some applications of
classication of low-dimensional Lie algebras // Book of abstracts of the International
mathematical conference dedicated to the 60th anniversary of the department of
algebra and mathematical logic of Taras Shevchenko National University of Kyiv,
14-17 July 2020, Kyiv, Ukraine. – 93 p. – [Electronic resource]. –
Access mode: https://bit.ly/2ZIyqMs – P. 34.
Phone number: (032) 258 96 63
E-mail: vasfed@gmail.com