Fedorchuk Volodymyr Ivanovych
Education:
Scientific degree: Ph.D. Degree
Position: Junior Research
Fellow
Research interests: finite-dimensional
Lie algebras, differential equations with non-trivial symmetry groups
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. Construction
of classes of first- and second- order differential equations in the space
M(1,4)× R(u) with non-trivial symmetry groups.
2. 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.M. Fedorchuk).
3. 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.M. Fedorchuk).
4. Classification
of all nonconjugate subalgebras (dimL ≤ 5) of the Lie algebra of the group P(1,4) in classes of isomorphic subalgebras. (With V.M. Fedorchuk).
5. 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.M. Fedorchuk).
6. Partial
preliminary group classification for nonlinear five-dimensional d’Alembert
equation.
7. Construction
of classes of invariant solutions for some five-dimensional d’Alembert
equations.
8. Classification
of symmetry reductions for the eikonal equation. (With V.M. Fedorchuk).
9. Classification of symmetry reductions for the
Euler-Lagrange-Born-Infeld equation. (With V.M. Fedorchuk).
10. Classification of symmetry reductions and invariant
solutions for the (1+3)-dimensional homogeneous and inhomogeneous
Monge-Ampère equati-ons. (With V.M. Fedorchuk).
Some of the important
publications:
Monographies
Vasyl Fedorchuk,
Volodymyr Fedorchuk. Classification of Symmetry Reductions for the Eikonal
Equation. - Lviv: Pidstryhach IAPMM of NAS of
Papers:
1. Fedorchuk V.I. First-order differential equations in the
space M(1,4)×R(u) with nontrivial symmetry groups. (Ukrainian) // Group
and analytic methods in mathematical physics (Ukrainian), 283–292, Pr. Inst.
Mat. Nats. Akad. Nauk Ukr. Mat. Zastos., 36, Natsional. Akad. Nauk Ukraini, Inst. Mat.,
2. Fedorchuk V.I. On second-order differential equations in
the space M(1,4)×R(u) with nontrivial symmetry groups. (Ukrainian) //
Mat. Metodi Fiz.-Mekh. Polya. – 2001. – 44, N. 4. – Ñ. 52–56.
3.
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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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
12. 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.
13. Fedorchuk
V.M.and Fedorchuk
V.I., On functional bases of
the first-order differential invariants for non-conjugate subgroups of the Poincaré group P(1,4) // Annales Academiae Paedagogicae Cracoviensis, Studia Mathematica VII (2008), 41–50.
14. 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.
15. 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;
translated in J. Math. Sci., 181 (2012), no. 3,
305–319.
16. Fedorchuk V.I. On
a partial preliminary group classification of the nonlinear five-dimensional
d’Alembert equation. (Ukrainian) // Mat. Metodi Fiz.-Mekh. Polya. – 2012. - 55,
N 3. – P. 35–43; translated in J. Math.Sci., 194 (2013), no. 2, 166–175.
17. 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.
18. Fedorchuk V.I. On
invariant solutions of some five-dimensional d’Alembert equations. (Ukrainian)
// Mat. Metodi Fiz.-Mekh. Polya. – 2014. – 57, N 4, 27–34. ; translated in
Journal of Mathematical Sciences, Vol. 220, No. 1, 27 - 37 (2017).
19. Vasyl
Fedorchuk and Volodymyr Fedorchuk., On
Classification of Symmetry Reductions for the Eikonal Equation // Symmetry
2016, 8(6), 51; 32pages, doi:10.3390/sym8060051.
20. 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.
21. 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.
22. V.M. Fedorchuk, V.I. Fedorchuk, On the
classification of symmetry reduc-tion 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
23. 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.
24. 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)
25. 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
26. 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.
V.I. Fedorchuk. On Differential Equations of First- and Second-Order in the Space
M(1,3)×R(u) with Nontrivial
Symmetry Groups // Proc. of the Fourth Internat. Conf. Symmetry in
Nonlinear Mathematical Physics (9-15 July 2001, Kyiv,
2.
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
3.
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.
4.
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.
5.
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.
6.
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.
7.
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.
8. Vasyl
M. Fedorchuk and
9.
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}-
10. 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.
11. Ôåäîð÷óê
Â.². Ïðî ïîïåðåäíþ ãðóïîâó êëàñèô³êàö³þ íåë³í³éíîãî ï'ÿòèâèì³ðíîãî ð³âíÿííÿ
ä'Àëàìáåðà, Êîíôåðåíö³ÿ ìîëîäèõ ó÷åíèõ "ϳäñòðèãà÷³âñüê³ ÷èòàííÿ"
(23-25 òðàâíÿ 2012 ðîêó, Ëüâ³â), Òåçè äîïîâ³äåé. – Ëüâ³â, 2012, Åëåêòðîííèé
ðåñóðñ: http://iapmm.lviv.ua/chyt2012/materials/48.pdf
12. 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
13. 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
14. Fedorchuk
V.I. On Exact Solutions of Some P(1,4)-Invariant d'Alembert Equations //
International conference of yang mathematics (Kyiv, june 3–6, 2015): Book of
abstracts. – Kyiv, 2015. –P. 118.
15. Fedorchuk
Volodymyr I. On invariant solutions of the five-dimensional Liouville equation
// Symmetry and Integrability of Equations of Mathematical Physics,
International workshop in honor of Wilhelm Fushchych (December 17-20, 2016,
Kyiv,
16. 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.
17. 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.
18. 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.
19. 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.
20. 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,
21. Volodymyr Fedorchuk. On Symmetry
Reduction of the Eikonal Equation. 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. 188.
http://www.iapmm.lviv.ua/mpmm2018/Volume
3.pdf.
22. Fedorchuk
V.². On symmetry reduction and
invariant solutions of the eikonal equation.
VI All-Ukrainian
B.V. Vasylyshyn mathematical conference "Nonlinear problems of analysis" (26-28 september 2018, Ivano-Frankivsk - Mykulychyn). Book of Abstracts. Ivano-Frankivsk,
23. 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}.
24. Volodymyr Fedorchuk, On some invariant
solutions 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/FedorchukV.html }.
25. 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
26. 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.
27.
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 * [Bucharest, Romania]. List of abstracts, p.2. http://www.mathem.pub.ro/dept/dgds-20/dgds-20.htm
28.
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, Lviv, Ukraine). Book of Abstracts. p.31. http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf
29.
Volodymyr Fedorchuk. On Symmetry Reduction and
Invariant Solutions of the Euler-Lagrange-Born-Infeld Equation. XI
International Skorobohatko Mathematical Conference (October 26-30, 2020, Lviv,
Ukraine). Book of Abstracts. p.32. http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf
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
Differenti-al 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
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E-mail: volfed@gmail.com