Fedorchuk Vasyl Maksymovych

Education: Uzhgorod State University (speciality - physics, 1974),

postgraduate study at the Institute of Mathematics of  Academy of Sciences of the USSR (1977-1979).

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 National Academy of Sciences of Ukraine, 2018. – 176pp. pdf

 

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 Institute of Mathematics of NAS of Ukraine, 2006,  3, N 2, 302-308.

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 International Geometry Center, Vol. 14, no. 3 (2021) pp. 206–218. https://doi.org/10.15673/tmgc.v14i3.2078

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:

  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 Institute of Mathematics, Kyiv, 2000, V.30, Part 1, P. 103-108.
  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 Institute of Mathematics, Kyiv, 2000, V.30, Part 1, P.109 -115.
  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. Singapore, 2010, p. 454.
  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}-Bolyai University, Cluj-Napoca, Romania), p. 43.
  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 Ukraine, p. 43.
  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 Ukraine (July 8 -13, 2013, L'viv, Ukraine) // Book of abstracts, L'viv, Ivan Franko National University of L'viv, p. 58.
  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, Krakόw, Poland.

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, Institute of Mathematics of NAS of Ukraine).\\ http://www.imath.kiev.ua/~appmath/Abstracts2016/Vasyl\_Fedorchuk.pdf

  1.  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.
  2.  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.
  3.  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.
  4.  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.

  1.  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.
  2.  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 Stefanyk Precarpathian National University, 2018. – p. 63.
  3.  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.
  4. 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.

  1. 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
  2. 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
  3. 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
  4. 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

 

Phone number: (032) 258 96 63

E-mail: vasfed@gmail.com