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

Scientific profiles

          ORCID:                           https://orcid.org/0000-0003-0164-2673

          Scopus:                           https://www.scopus.com/authid/detail.uri?authorId=16491124400

          Google Scholar:               https://nbuviap.gov.ua/bpnu/bpnu_profile.php?bpnuid=BUN0006656

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., Fedorchuk, V.I. On Partial Preliminary Group Classification for Some Class of (1+3)-Dimensional Monge–Ampère Equations. I. One-Dimensional Lie Algebras. // Journal of Mathematical Sciences. – 2025. – 291, Issue 5. – P. 608–616. https://doi.org/10.1007/s10958-025-07840-y (Scopus, Q3)
  2. Fedorchuk V.M., Fedorchuk V.I. On the Construction and Classification of the Common Invariant Solutions for the (1+3)-Dimensional Euler – Lagrange – Born – Infeld and Homogeneous Monge – Ampère Equations // Mat. Metody Fiz.–Mekh. Polya. – 2024. – 67, ¹ 1–2. – P. 15–24. doi: 10.15407/mmpmf2024.67.1-2.15-25 (in Ukrainian)
  3. Fedorchuk V.M., Fedorchuk V.I. On the Symmetry Reduction of the (1+3)-Dimensional Inhomogeneous Monge–Ampère Equation to Algebraic Equations // Journal of Mathematical Sciences. – 2024. – 282, No.5. – P. 668–677. https://doi.org/10.1007/s10958-024-07208-8 (Scopus, Q3)
  4. Fedorchuk V.Ì., Fedorchuk V.I. On the Classification of Symmetry Reductions for the (1+3)-Dimensional Monge-Ampère Equation. // Journal of Mathematical Sciences. – 2023. – 272, No. 1. – P. 1–13. https://doi.org/10.1007/s10958-023-06395-0 (Scopus, 0.302, Q3)
  5. Fedorchuk V.M., Fedorchuk V.I. On the Construction and Classification of the Common Invariant Solutions for Some P(1,4) - Invariant Partial Differential Equations // Applied Mathematics. – 2023 – Vol. 14, No.11 – P. 728–747. https://doi.org/10.4236/am.2023.1411044 (Scopus, 0.228, Q4)
  6. Fedorchuk V.M., Fedorchuk V.I. On partial preliminary group classification of some class of the (1+3)–dimensional Monge – A mpère equations. I. One–dimensional Lie algebras // Mat. Metody Fiz.–Mekh. Polya. – 2023. – 66, ¹ 1–2. – P. 40–47. (in Ukrainian)
  7. Fedorchuk V.M., Fedorchuk V.I. on symmetry reduction of the (1+3)–dimensional inhomogeneous Monge – Ampère equation to algebraic equations // Mat. Metody Fiz.–Mekh. Polya.  – 2022. –  65, ¹ 1–2. – P. 58–64. (in Ukrainian)
  8. 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. (Scopus, 0.726, Q3)
  9. 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)
  10. Fedorchuk, V., Fedorchuk, V. Ñèìåòð³éíà ðåäóêö³ÿ òà äåÿê³ êëàñè ³íâàð³àíòíèõ ðîçâ’ÿçê³â (1+3)-âèì³ðíîãî îäíîð³äíîãî ð³âíÿííÿ Ìîíæà-Àìïåðà // Proceedings of the International Geometry Center. − 2021. − 14 (3). − 206–218. https://doi.org/10.15673/tmgc.v14i3.2078 (Scopus, 0.603, Q4)
  11. 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)
  12. 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. (Google Scholar, 0.507, Q4)
  13. Fedorchuk V.M., Fedorchuk V.I. On the classification of symmetry reduction and invariant solutions for the Euler-Lagrange-Born-Infeld equation. // Ukrainian Journal of Physics. − 2019. − 64, ¹ 12. − P. 1103−1107. https://doi.org/10.15407/ujpe64.12.1103 (Scopus, 0.333, Q4)
  14. Fedorchuk V.M., Fedorchuk V.I., On symmetry reduction of the Euler–Lagrange–Born–Infeld equation to linear ODEs // Symmetry and Integrability of Equations of Mathematical Physics, Collection of Works of Institute of Mathematics, Kyiv. − 2019. − 16, ¹ 1. − P. 193−202.
  15. 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, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, Lviv, 2017. – P. 241–255.
  16. Vasyl Fedorchuk and Volodymyr Fedorchuk, On Classification of Symmetry Reductions for the Eikonal Equation //  Symmetry 2016, 8(6), 51; 32pages, doi:10.3390/sym8060051.
  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. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. Fedorchuk V, On invariants of continuous subgroups of the generalized Poincaré group P(1,4) // Universitatis Iagellonicae Acta Mathematica, Fasciculus XL, 2002, 197-205.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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).
  34. 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.
  35. 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.
  36. 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.
  37. 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).
  38. 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).

 

Conference proceedings:

1.     Vasyl Fedorchuk, Volodymyr Fedorchuk. On the construction and classification of the common invariant solutions for the (1 + 3)-dimensional Euler-Lagrange-Born-Infeld and homogeneous Monge-Ampere equations // International scientific online conference «Algebraic and geometric methods of analysis», May 27-30, 2024, Odesa, Ukraine. – P. 33–34. https://imath.kiev.ua/~topology/conf/agma2024/abstracts/texts/fedorchuk/fedorchuk.pdf

2.     Vasyl Fedorchuk, Volodymyr Fedorchuk, On the construction of the common invariant solutions for some P(1,4)-invariant partial differential equations // International conference dedicated to the 145th anniversary of the birth of Hans Hahn, September 23–27, 2024, Chernivtsi. – Chernivtsi: Yuriy Fedkovych Chernivtsi National University, 2024. – 184 p. – P. 129. https://hahn.chnu.edu.ua/media/3cln1ko5/book-of-abstracts.pdf

3.     Fedorchuk Vasyl, Fedorchuk Volodymyr. On Classification of Symmetry Reductions for Some P(1,4)-Invariant Partial Differential Equations. Symmetry 2023 - The 4th International Conference on Symmetry (21 – 23 June, 2023, AXA Convention Centre Barcelona, Spain). Program and Abstract Book, p.49. https://symmetry2023.sciforum.net/events_files/766/customs/af8bdf95fc6ca8768ff2b5bbc213cf7f.pdf

4.     Fedorchuk Vasyl, Fedorchuk Volodymyr. Classification of symmetry reductions for some P(1,4)-invariant partial differential equations. // Int. Scientific Conference “Current Problems of Mechanics and Mathematics – 2023” (May 23–25, 2023, Lviv, Ukraine) http://iapmm.lviv.ua/mpmm2023/materials/proceedings.mpmm2023.pdf, P. 376. http://iapmm.lviv.ua/mpmm2023/materials/ma09_02.pdf

5.     Fedorchuk Vasyl, Fedorchuk Volodymyr. On partial preliminary group classification of some class of (1 + 3)-dimensional Monge-Ampere equations. Two-dimensional Abelian Lie algebras // International Online Conference Algebraic and geometric methods of analysis (May 29 June 31, 2023, Odesa-Kyiv, Ukraine)} https://imath.kiev.ua/~topology/conf/agma2023/contents/abstracts/texts/fedorchuk/fedorchuk.pdf.

6.     Fedorchuk Vasyl, Fedorchuk Volodymyr. 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

7.     Fedorchuk Vasyl, Fedorchuk Volodymyr. On patrial preliminary group classification of some class of (1+3)-dimensional Monge-Ampere equations. I. One-dimensional Lie algebras // Workshop "Symmetry and Integrability of Equations of Mathematical Physics" December 23-24, 2022, Kyiv, Ukraine. http://www.imath.kiev.ua/~appmath/Abstracts2022/Fedorchuk.pdf

8.     Fedorchuk Vasyl, Fedorchuk Volodymyr. On patrial preliminary group classification of some class of (1+3)-dimensional Monge-Ampere equations. One-dimensional Galilean Lie algebras // International Scientific Conference "Algebraic and Geometric Methods of Analysis" Odesa, Ukraine May 24-27, 2022. http://imath.kiev.ua/~topology/conf/agma2022/contents/abstracts/texts/fedorchuk/fedorchuk.pdf – P. 16–17.

9.     Fedorchuk Vasyl, Fedorchuk Volodymyr. 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

10. Fedorchuk Vasyl, Fedorchuk Volodymyr. 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

11. Fedorchuk V. M., Fedorchuk V. I. 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. – Ðåæèì äîñòóïó äî ðåñóðñó: https://bit.ly/2ZIyqMs – P. 34.

12. Fedorchuk Vasyl, Fedorchuk Volodymyr. 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

13. Fedorchuk Vasyl, Fedorchuk Volodymyr. 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

14. Fedorchuk V. M. and Fedorchuk V. I.  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

15. Fedorchuk Vasyl. 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. – Access mode: (http://www.iapmm.lviv.ua/mpmm2018/Volume_3.pdf). P. 187.

16. 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.

17. Fedorchuk Vasyl, Fedorchuk Volodymyr. 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.

18. 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.

19. Fedorchuk Vasyl, Fedorchuk Volodymyr, 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.

20. Fedorchuk Vasyl and Fedorchuk Volodymyr. 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. Fedorchuk Vasyl. 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.

22. Fedorchuk Vasyl, Fedorchuk Volodymyr. 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.

23. Fedorchuk V.M. , Fedorchuk V.I.  On Classification of Some Non-Singular Manifolds In the Space M(1,3) ×R(u). // BGL17: 10th Bolyai-Gauss-Lobachevski Conference on Non-Euclidean Geometry and its Applications. (Aug 20–26, 2017 Gyöngyös, Hungary). https://indico.cern.ch/event/586799/attachments/1400831/2353974/bgl17_preliminary_agenda.pdf.

24. 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.

25. 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

26. 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.

27. 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

28. 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.

29. 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.

30. 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.

31. 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.

32. 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.

33. 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.

34. 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.

35. 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.

36. 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.

37. 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.

38. 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.

39. 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, Kyiv, Ukraine), Proceedings of Institute of Mathematics, Kyiv, 2000, V.30, Part 1, P.109 -115.

40. 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.

 

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