Fedorchuk Vasyl' Maksymovych
Education: Uzhgorod State University
(speciality - physics, 1974),
postgraduate study at the
Scientific title: senior researcher
(1990)
Scientific degree: Doctor of Sciences
(1999)
Position: Leading Researcher
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).
The results obtained are presented in 118 scientific publications (65 articles, 53 abstracts).
Major publications:
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.
List
of Conference Proceedings:
1.
Fedorchuk V.M., Fedorchuk I.M. and Fedorchuk V.I., On Symmetry Reduction of the Five-Dimensional Dirac Equation // The
Third Internat. Conf. "Symmetry in Nonlinear
Mathematical Physics" (July 12-18, 1999, Kyiv, Ukraine), Proceedings of
2.
Fedorchuk V.M. and Leibov O.S., On Symmetry Reduction and Some Exact Solutions
of the Multidimensional Born-Infeld Equation // The Third Internat. Conf.
"Symmetry in Nonlinear Mathematical Physics" (July 12-18,
1.
Fedorchuk V., Invariants of
continuous subgroups of the generalized Poincaré
group P(1,4) and differential equations in the space M(1,4)× R(u) // Acta Universitatis Purkynianae 72, Studia Mathematica, Czech-Polish Mathematical School 2001, Usti nad Labem, 2001, 15-20.
2.
FedorchukV.M. and Fedorchuk V.I., Subgroup structure of the generalized Poincaré group P(1,4) and
models with nontrivial symmetry // Mathematical physics: Proceedings of the
Ukrainian mathematical congress - 2001.
- Kyiv: Institute of mathematics of NAS of Ukraine, 2002, 101-116.
3.
Fedorchuk V. and Fedorchuk V., Some new differential equations of the
first-order in the spaces M(1,3)× R(u) and M(1,4)× R(u) with given
symmetry groups // Functional Analysis and its Applications, North-Holland
Mathematics Studies, 197, Editor: Saul Lubkin,
Elsevier, 2004, 85-95.
4.
Fedorchuk V.I. and Fedorchuk V.M., Symmetry reduction of some classes of the
first-order differential equations in the space M(1,4)× R(u) // XIth Slovak-Polish-Czech Mathematical School, Mathematica, Proceedings of the XIth
Slovak-Polish-Czech Mathematical School (Ruzomberok,
June 2nd-5th, 2004), Pedagogical Faculty of Catholic University in Ruzomberok, P. 37-41.
5.
Fedorchuk V.M. and Fedorchuk V.I., On first-order differential invariants of
the non-conjugate subgroups of the Poincaré
group P(1,4) // Differential Geometry and its Applications: Proc. 10th Int.
Conf. on DGA
6.
Fedorchuk V.M. and Fedorchuk V.I., On non-equivalent functional bases of
first-order differential invariants of the non-conjugate subgroups of the Poincaré group P(1,4) // Acta Physica Debrecina,
2008, XLII, 122-132.
7.
Vasyl M. Fedorchuk and Volodymyr I. Fedorchuk., On some classes of the partial differential
equations with non-trivial symmetry groups // Proc. of the XVIth
International Congress on Mathematical Physics, edited by Pavel
Exner, World Scientific Publishing Co. Pte. Ltd.
8.
Vasyl Fedorchuk and Volodymyr Fedorchuk., On
non-singular manifolds in the space M(1,3)×R(u) invariant under the
non-conjugated subgroups of the Poincaré group
P(1,4) // The 7th edition of the Bolyai-Gauss-Lobachevsky
conference series. Abstracts book. International Conference on Non-Euclidean
Geometry and its Applications (5-9 July 2010, Babe\c{s}-
Phone number: (032) 258 96 22
E-mail: vasfed@gmail.com