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)
Translation: Fedorchuk V.M. ,
Fedorchuk V.I. Reduction of the (1 + 3)-dimensional Inhomogeneous
Monge–Ampère equation to first-order partial differential equations //
Ukr. Mat. J. – 2022. – 74, No. 3. – P. 472–483. – https://doi:10.1007/s11253-022-02076-4.
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, 1999 in Kyiv, Ukraine), Proceedings of
3.
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.
4.
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.
5.
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.
6.
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.
7.
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 2007, in Honour of Leonhard Euler, Olomouc, Czech
Republic, 27 - 31 August 2007, World Scientific Publishing Company, 2008,
431-444.
8.
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.
9.
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.
10. 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}-
11. Vasyl
M. Fedorchuk, Volodymyr I. Fedorchuk, Classification of the five-dimensional
non-conjugate subalgebras of the Lie algebra of the Poincaré group
P(1,4), 8th International Algebraic Conference in Ukraine (July
5-12, 2011, Lugansk, Ukraine), Book of abstracts, Lugansk, Lugansk Taras
Shevchenko National University, p. 160.
12. Fedorchuk
V.M, Fedorchuk V.I., Classification of non-singular manifolds in the space
M(1,4)×R(u) invariant under one- and two-dimensional non-conjugate
subalgebras of the Lie algebra of the Poincaré group P(1,4) // 8th Bolyai-Gauss-Lobachevsky
Conference "Non-Euclidean Geometry in Modern Physics and Mathematics"
(Uzhgorod, Ukraine, 22-25 May
2012). Programme and Abstracts.
Uzhgorod, 2012, IEP of the NAS of
13. Fedorchuk
V.M., Fedorchuk V.I. Classification of low-dimensional noncon-jugate
subalgebras of the Lie algebra of the Poincaré group P(1,4), 9-th Inter-national Algebraic Conference in
14. Vasyl Fedorchuk, Volodymyr Fedorchuk, On
Symmetry Reduction of Some P(1,4)-invariant Differential Equations, Abstracts
of The XVIth International Conference is Dedicated to 70th Anniversary of
Professor Jan J. Sławianowski (June 6-11, 2014, Varna, Bulgaria),
Institute of Biophysics, Bulgarian Academy of Sciences,\\ http://www.bio21.bas.bg/conference/Conference\_files/abstr2014/Fedorchuk.pdf
15. V.
Fedorchuk, V. Fedorchuk, On symmetry reduction and invariant solutions of some
P(1,4)-invariant differential equations, Abstracts of the 14th Conference
"Mathematics in Technical and Natural Sciences” (September 18-24, 2015,
Kościelisko), Faculty of Applied Mathematics of AGH University of Science
and Technology,
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,
17. Vasyl Fedorchuk. O klasyfikacji niskowymiarowych algebr Liego,
abstrakty Drugiej Ogόlnopolskej Konferencji Naukowej "Oblicza Algebry
II" (Krakόw, 1-4 czerwca, 2017), Uniwersytet Pedagogiczny im. KEN w
Krakowie,\\
http://algebra.up.krakow.pl/II/files/abstrakty.pdf, S. 15.
18. Fedorchuk V.M., Fedorchuk V.I.
Classification of low-dimensional Lie Algebras, Abstracts of the 11th
International Algebraic Conference in Ukraine dedicated to the 75th anniversary
of V.V.Kirichenko (July 3-7, 2017, Kyiv, Ukraine), Taras Shevchenko National
University of Kyiv, p. 42.
19. Vasyl Fedorchuk, Volodymyr Fedorchuk. On Ñlassification of Symmetry Reductions for Partial
Differential Equations, Program and Abstract Book. Symmetry 2017: The 1st
International Conference on Symmetry (16-18 October 2017, Parc Cientific de
Barcelona, Spain), MDPI, p. 168.
20. Vasyl Fedorchuk and Volodymyr Fedorchuk. On Classification of Symmetry Reductions for Partial
Differential Equations \\ www.mdpi.com/2504-3900/2/1/85; \\ Proceedings 2018,
2(1), 85; https://doi.org/10.3390/proceedings2010085.
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.
23. Vasyl Fedorchuk, Volodymyr Fedorchuk. On classification of some non-singular manifolds in
the space M(1,3)× R(u) and symmetry reduction of the eikonal equation.
The XII-th International Conference of Differential Geometry and Dynamical
Systems (DGDS-2018) (30 August - 2 September 2018, the Callatis High-School in
the city Mangalia - Romania). Abstracts. - p. 1., http://www.mathem.pub.ro/dept/dgds-18/dgds-18.htm.
24. Fedorchuk
V.M., Fedorchuk V.I. On symmetry reduction of some partial differential
equations. VI All-Ukrainian B.V. Vasylyshyn
mathematical conference "Nonlinear problems
of analysis" (26-28 september 2018, Ivano-Frankivsk - Mykulychyn). Book of Abstracts. Ivano-Frankivsk,
- Vasyl Fedorchuk,
Volodymyr Fedorchuk, On classification of symmetry reductions for the
Euler–Lagrange–Born–Infeld equation // Symmetry and Integrability of
Equations of Mathematical Physics, International workshop on the occasion
of the fortieth anniversary of the Department of Applied Research
(nowadays the Department of Mathematical Physics) (December 21-24, 2018,
Kyiv, Institute of Mathematics of NAS of Ukraine). https://www.imath.kiev.ua/~appmath/Abstracts2018/Fedorchuk.html.
- V. M. Fedorchuk and
V. I. Fedorchuk. On classification
of symmetry reductions and invariant solutions for the
Euler-Lagrange-Born-Infeld equation. Book of Abstracts. Kiev, Bogolyubov
Institute for Theoretical Physics of NAS of Ukraine, 2019, P.10. https://indico.bitp.kiev.ua/event/3/attachments/1/83/abstr_bgl_2019.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.
28. Vasyl
Fedorchuk, Volodymyr Fedorchuk. On symmetry reduction and some classes of
invariant solutions of the (1+3)-dimensional Monge-Ampère equation. The
XIV-th International Conference of Differential Geometry and Dynamical Systems
( DGDS-2020 ) 27 -29 August 2020 * ONLINE * [
29. Vasyl
Fedorchuk, Volodymyr Fedorchuk. On Classification of Symmetry Reductions for
Some P(1,4)-Invariant Partial Differential Equations. XI International
Skorobohatko Mathematical Conference (October 26-30, 2020,
30. Vasyl Fedorchuk, Volodymyr Fedorchuk. On
symmetry reduction and some classes of invariant solutions of the (1 +
3)-dimensional homogeneous Monge-Ampère
equation. International On line Conference Algebraic and Geometric Methods of
Analysis dedicate to the memory of Yuriy Trokhymchuk (17.03.1928-18.12.2019)
(May 25-28, 2021, Odesa, Ukraine). Book of Abstracts. p.36 https://www.imath.kiev.ua/~topology/conf/agma2021/contents/agma2021-abstracts.pdf
31. Vasyl Fedorchuk, Volodymyr Fedorchuk. On
symmetry reduction and some classes of invariant solutions of the
(1+3)-dimensional inhomogeneous Monge-Ampère equation. The XV-th International Conference of Differential
Geometry and Dynamical Systems (DGDS-2021)
26 - 29 August 2021 * ONLINE * [Bucharest, Romania]. The booklet of
abstracts. p.5 http://www.mathem.pub.ro/dept/dgds-21/dgds-21.htm
32. Vasyl
Fedorchuk, Volodymyr Fedorchuk. On symmetry reduction of the (1+3)-dimensional
Inhomogeneous Monge-Ampère equation to algebraic equation. The XVI-th
International Conference of Differential Geometry and Dynamical Systems (
DGDS-2022 ), (1 - 4 September 2022) * ONLINE * [Bucharest, Romania]. The
booklet of abstracts. p. 10. \\ http://www.mathem.pub.ro/dept/dgds-22/dgds-22.htm
Phone number: (032) 258 96 63
E-mail: vasfed@gmail.com