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 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 (dimL5) 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 (dimL5) 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. 717722. English translation: Ukrainian Math. J., 31 (1979), no. 6, 554558 (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. 28932899.

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. 2426.

5.      Fedorchuk V. Symmetry Reduction and Exact Solutions of the Euler-Lagrange-Born-Infeld, the Multidimensional MongeAmpère and the Eikonal Equations // J. Nonlinear Math. Phys. 1995. v. 2, N 34. P. 329333.

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. 574577; translation in Ukrainian Math. J., 48 (1996), no. 4, 636640 (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. 2429.

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. 3642.

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), 4150.

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, 2. P. 23-27 ; translation in J. Math. Sci., 170 (2010), no. 5, 588593.

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, 305319.

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 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.

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 2007, in Honour of Leonhard Euler, Olomouc, Czech Republic, 27 - 31 August 2007, World Scientific Publishing Company, 2008, 431-444.

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. Singapore, 2010, p. 454.

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}-Bolyai University, Cluj-Napoca, Romania), p. 43.

Phone number: (032) 258 96 22

E-mail: vasfed@gmail.com