Iryna YEHORCHENKO
Address:
Institute
of Mathematics
National
Academy
of Sciences
of Ukraine
3
Tereshchenkivs'ka Street
01024
Kyiv
UKRAINE
E-mail: iyegorch@imath.kiev.ua
Academic
Background:
Ph.D.
in Math.:
1989, Institute of Mathematics, Kyiv (Supervisor Prof. W.I.
Fushchych) Symmetry
analysis of nonlinear equations for complex scalar and vector
fields
M.Sc.
in Math.:
1984, Kyiv National
University
Professional
Experience: 1985-till
now
Senior
Researcher
at the Department of
Applied Research of
the Institute of
Mathematics, National Academy of
Sciences, Kyiv
ORCID 0000-0001-6442-4812
AREA OF EXPERTISE: mathematical physics, symmetry analysis of PDE; Lie algebras and Lie groups; symmetry, reduction and exact solutions of nonlinear PDE; nonlocal, potential and nonclassical symmetries of PDE; point transformations and equivalence problems in classes of PDE; theory of differential invariants
MOST IMPORTANT RESEARCH RESULTS: classification of differential invariants of the Euclid, Poincare, Lorentz, conformal, Galilei algebras for arbitrary dimensions and arbitrary sets of scalar functions; definition and study of conditional differential invariants; efficient procedure for classification of relative differential invariants, concept of extension for realizations of first-order differential operator algebras; classification of invariant equations and analytical solutions for equations of mathematical physics; necessary conditions of compatibility of the d’Alembert and Hamilton equations for arbitrary dimensions and one and two functions; general solution of the system of coupled eikonal equations; differential invariants of the nonlinear realisation of the Poincare algebra; efficient procedure for classification of differential invariants of infinite-dimensional algebras; general parametric solutions of many nonlinear systems of PDE. Presented talks at over 50 international conferences.
Other activities:
Member of the Organising Committee of the conferences ``Symmetry in Nonlinear Mathematical Physics''
(Kyiv, Ukraine, 1995, 1997, 1999, 2001, 2003, 2005, 2007, 2009)
Associate Editor, SIGMA
Member of the Organising Committee of the Voronoi Conferences (Kyiv, Ukraine, 1993, 1998, 2003, 2008, 2013, 2018)
Reviewer, Mathematical Reviews
Presented talks at numerous international conferences on evaluation of research and research policies. Founder and member of two NGOs working in promoting of good practices in science and education, and improvement of policies in these fields; and in attraction of girls to STEM professional fields. Participated in numerous working groups at the NASU and Parliament of Ukraine on science and education policies. Taught at mathematical circles for school students, served as an evaluation board member of school student mathematical competitions. Gave numerous talks on popular mathematics for various audiences, including lectures at training courses for teachers of mathematics; organised popular mathematics events. Published over 30 papers in major Ukrainian media on popular mathematics and science and education policies; gave numerous interviews for Ukrainian and international media, including major journals “Science” and “Nature”. A member of the Ukrainian initiative “UAScience.reload” facilitating assistance to Ukrainian researchers affected by the Russian aggression, and reconstruction of Ukrainian science potential.
PUBLICATIONS
1. Yehorchenko I.A., Extension of Realisations for Low-Dimensional Lie Algebras and Relative Differential Invariants, arXiv:2212.05657
2. Yehorchenko I.A., Eikonal Equation 0.1, arXiv:2212.09914
3. Yehorchenko I.A., A.I. Vorobyova, Conditional and Hidden Infinite-Dimensional Symmetries of Wave Equations, Ukrainian Mathematical Journal . Aug2022, Vol. 74 Issue 3, p.378-384.
4. Yehorchenko I.A., Differential invariants, hidden and conditional symmetry, Ukr Math J 73, 1189–1199 (2022).
5. Yehorchenko I.A., Solutions of the system of coupled eikonal equations, Collection of Papers of the Institute of Mathematics of NAS of Ukraine, 2019, p.66-77.
6. Yehorchenko I.A., Invariants for sets of vectors and rank 2 tensors, and differential invariants for vector functions, arXiv:1812.02918
7. Yehorchenko I.A., General Solution for a Coupled System of Eikonal Equations in Two Space Variables, arXiv:1712.01948
8. Yehorchenko I.A., Solutions of the system of d'Alembert and eikonal equations, and classification of reductions of PDEs, 2015 J. Phys.: Conf. Ser. 621 012018
9. Yehorchenko I.A., Ansatzes and exact solutions for nonlinear Schrodinger equations, arXiv:1412.1889
10. Yehorchenko I.A., Comment to" General Solution to Unidimensional Hamilton-Jacobi Equation"[arXiv: 1302.0591 v1], arXiv:1304.3515
11. Yehorchenko I.A. Reduction of Multidimensional Wave Equations to Two-Dimensional Equations: Investigation of Possible Reduced Equations, Proceedings of the 5th Workshop "Group Analysis of Differential Equations & Integrable Systems", Protaras, Cyprus, 2011, p. 225-235, arXiv:1010.4977
12. Yehorchenko I.A. Differential Invariants and Hidden Symmetry, arXiv:1010.5313
13. Yehorchenko I.A. Conditional Symmetry and Reductions for the Two-Dimensional Nonlinear Wave Equation. I. General Case, arXiv:1010.4913
14. Yehorchenko I.A. Reduction of non-linear d'Alembert equations to two-dimensional equations, Proceedings of the 4th Workshop "Group Analysis of Differential Equations & Integrable Systems", Protaras, Cyprus, 2009, p. 243-253, arXiv:0910.2501
15. Yehorchenko I.A., Vorobyova A.I. Infinite-dimensional symmetry for wave equation with additional condition, arXiv:0910.2380
16. Yehorchenko I.A. Differential Invariants of Infinite-Dimensional Algebras That Are Equivalence Algebras of Classes of PDE, Bulg. J. Phys. vol.35 no.1 (2008), p. 481-488, arXiv:0910.2208
17. Yehorchenko I.A. General Results on Conditional Symmetry for the Two-Dimensional Nonlinear Wave Equation, arXiv:0910.1946
18. Yehorchenko I.A. Relative invariants for Lie algebras: construction and applications, Symmetry and Perturbation Theory, Proceedings of the International Conference on SPT 2007. Otranto, Italy, 2 - 9 June 2007, G. Gaeta, R. Vitolo and S. Walcher (Eds.), World Scientific (2007), p. 282-284
19. Yehorchenko I.A. Reduction of multidimensional non-linear d'Alembert equations to two-dimensional equations: ansatzes, compatibility of reduction conditions, Collection of Papers Dedicated to 70th Anniversary of W.I. Fushchych, Kyiv, Institute of Mathematics, 2006, p. 81-95, arXiv:math-ph/0611003
20. Yehorchenko I.A. Differential invariants for infinite-dimensional algebras, in Proceedings of the International Conference on SPT 2004, Cala Gonone, Sardinia, Italy, May 30 – June 6, 2004; Editors G. Gaeta, B. Prinari, S. Rauch-Wojciechowski and S. Terracini, World Scientific, 2005, p. 308-312 [pdf] (see math-ph/0607002).
21. Yehorchenko I.A. Group classification with respect to hidden symmetry, in Proceedings of Fifth International Conference ``Symmetry in Nonlinear Mathematical Physics'' (June 23-29, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko, Kyiv, Institute of Mathematics, 2004, V.50, Part 1, 290-297 [pdf].
22. Yehorchenko I.A., Vorobyova A.I. Sets of conditional symmetry operators and exact solutions for wave and generalised heat equations., in Proceedings of Fifth International Conference ``Symmetry in Nonlinear Mathematical Physics'' (June 23-29, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko, Kyiv, Institute of Mathematics, 2004, V.50, Part 1, 298-303 [pdf].
23. Yehorchenko I.A. Differential invariants and construction of conditionally invariant equations, Symmetry in nonlinear mathematical physics, Part 1, Proceedings of Inst. Mathematics of National Acad. Science of Ukraine (Kyiv, 2001), 2002, V. 43, 256-262 [pdf] (see math-ph/0304029).
24. Popovych R.O., Yehorchenko I.A. Group classification of generalized eikonal equations, Ukrainian Math. Journal, 2001, V. 53, N 11, 1513-1520 (in Ukrainian); translation in Ukrainian Math. J., 2001, V. 53, N 11, 1841-1850 (see math-ph/0112055).
25. Vasilenko O.F., Yehorchenko I.A. Group classification of multidimensional nonlinear wave equations, Group and analytic methods in mathematical physics, Proceedings of Inst. Mathematics of National Acad. Science of Ukraine, Kyiv, 2001, V. 36, 63-66 (in Ukrainian) [pdf].
26. Yehorchenko I.A. On symmetry of a class of first order PDEs, Symmetry in nonlinear mathematical physics, Part 1, 2, Proceedings of Inst. Mathematics of National Acad. Science of Ukraine (Kyiv, 1999), 2000, V. 30, 245-248 [pdf].
27. Yehorchenko I.A. Ansatzes and exact solutions for nonlinear Schrödinger and wave equations, Symmetry and analytic methods in mathematical physics (in Ukrainian), Inst. Mathematics of National Acad. Science of Ukraine, Kyiv, 1998, V. 19, 80-87 [pdf].
28. Yehorchenko I.A. Differential invariants for a nonlinear representation of the Poincaré algebra. Invariant equations, Symmetry in nonlinear mathematical physics, Vol. 1, 2, National Acad. Science of Ukraine (Kyiv), 1997, 200-205 [pdf].
29. Yehorchenko I.A. New nonlinear Poincare-invariant equations, Proceedings of the XXI Colloquim "Group Theory the Physics", Goslar, Germany, 1996, World Scientific, 1997, p. 1022-1026
30. Yehorchenko I.A. Second-order differential invariants for some extensions of the Poincaré group and invariant equations, J. Nonlin. Math. Phys., 1996, V. 3, no. 1-2, 186-195 [pdf].
31. Fushchych W.I. and Yehorchenko I.A. New conditionally invariant solutions for non-linear d'Alembert equation, Preprint LiTH–MAT–R–93–07, Linköping University, Sweden, 1993, 9 p. [pdf].
32. Yehorchenko I.A. Second-order differential invariants for the Poincaré, Galilei and conformal algebras in many-dimensional spaces, Classical and quantum systems (Goslar, 1991), World Sci. Publishing, River Edge, NJ, 1993, 738-741.
33. Yehorchenko I.A. Nonlinear representation of the Poincaré algebra and invariant equations, Symmetry analysis of equations of mathematical physics, Nat. Acad. Sci. Ukraine, Inst. Math., Kyiv, 1992, 62-65.
34. Fushchych W.I. and Yehorchenko I.A. Second-order differential invariants of the rotation group O(n) and of its extensions: E(n); P(1,n); G(1,n), Acta Appl. Math., 1992, V. 28, N 1, 69-92 [pdf].
35. Yehorchenko I.A., Vorobyova A.I. Conditional invariance and exact solutions of the Klein-Gordon-Fock equation, Reports of Acad. Science of Ukraine, 1992, N 1, 19-22, 176 (in Ukrainian).
36. Yehorchenko I.A., Vorobyova A.I. Conditional invariance and exact solutions of a nonlinear heat equation, Reports of Acad. Science of Ukraine, 1992, N 3, 20-22, 160 (in Ukrainian).
37. Fushchych W.I. and Yehorchenko I.A. Non-Lie ansätze and conditional symmetry of the nonlinear Schrödinger equation, Ukrainian Math. Journal, 1991, V. 43, N 12, 1620-1628 (in Ukrainian); translation in Ukrainian Math. J., 1991, V. 43, N. 12, 1507-1515 [pdf].
38. Fushchych W.I., Zhdanov R.Z. and Yehorchenko I.A. On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton system, J. Math. Anal. Appl., 1991, V. 161, N 2, 352-360 [pdf].
39. Fushchych W.I., Yehorchenko I.A. Reduction and solutions of a nonlinear equation for the vector potential, Reports of Acad. Science of Ukr. SSR, Ser. A, 1991, N 4, 23-25, 158 (in Ukrainian) [pdf].
40. Yehorchenko I.A. Exact solution of the non-linear d'Alembert equation. In the book: Symmetries and Algebraic Structures in Physics, Proceedings of the XVIII International Colloquium on Group Theoretical Methods in Physics, Moscow, USSR, June 4-9, 1990, Vol. 2, V.V. Dodonov. and V. Man'ko Eds, Nova Science, Singapore, 1991, p.55-58 (see on GoogleBooks)
41. Fushchych V.I., Yehorchenko I.A. Reduction of a multidimensional nonlinear wave equation to two-dimensional equations, Reports of Acad. Science of Ukr. SSR, Ser. A, 1990, N 8, 32-34, 86 (in Ukrainian) [pdf] (see math-ph/0610020).
42. Yehorchenko I.A. Differential invariants of Euclidean algebra, Ukrainian Math. Journal, 1990, V. 42, N 6, 767-772 (in Ukrainian); translation in Ukrainian Math. J., 1990, V. 42, no. 6, 676-681.
43. Yehorchenko I.A. Stationary solutions of the nonlinear wave equation, Algebra-theoretic analysis of equations in mathematical physics, Acad. of Science of Ukr. SSR, Institute of Mathematics, Kyiv, 1990, 26-30 (in Russian).
44. Yehorchenko I.A. Exact solutions of the nonlinear Schrödinger equation, Symmetry and solutions of equations of mathematical physics, Acad. of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1989, 17-20 (in Russian).
45. Yehorchenko I.A. Symmetry properties of nonlinear equations for a complex vector field, Acad. Science of Ukr. SSR, Kyiv, Inst. Mat. Preprint N 89.48, 1989, 39 p. (in Russian).
46. Fushchych W.I. and Yehorchenko I.A. Differential invariants of the Poincaré algebra and of the conformal algebra, Reports of Acad. Science of Ukr. SSR, Ser. A, 1989, N 5, 21-22 (in Ukrainian) [pdf].
47. Fushchych W.I. and Yehorchenko I.A. Differential invariants of the Galilei algebra, Reports of Acad. Science of Ukr. SSR, Ser. A, 1989, N 4, 29-32, 86 (in Ukrainian) [pdf].
48. Fushchych W.I. and Yehorchenko I.A. The symmetry and exact solutions of the nonlinear d'Alembert equation for complex fields, J. Phys. A, 1989, V. 22, N 14, 2643-2652 [pdf].
49. Yehorchenko I.A., Vorobyova A.I. Exact solutions of the wave equation with additional conditions, Symmetry and solutions of equations of mathematical physics, Acad. of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1989, 21-25 (in Russian).
50. Yehorchenko I.A. Complex generalization of the Hamilton-Jacobi equation and its solutions, Symmetry analysis and solutions of equations of mathematical physics, Acad. of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1988, 4-8 (in Russian).
51. Fushchych W.I., Yehorchenko I.A. Symmetric properties of complex-valued nonlinear wave equations, Reports of Acad. Science of USSR, 1988, V. 298, N 2, 347-351 (in Russian) [pdf]; translation in Soviet Phys. Report, 33 (1988), N 1, 36-38.
52. Yehorchenko I.A. Particular solutions of two systems of nonlinear multidimensional wave equations, Symmetry and solutions of nonlinear equations of mathematical physics, Acad. of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1987, 47-54 (in Russian).
53. Yehorchenko I.A. Poincaré-invariant quasilinear wave equations for complex-valued functions, Acad. Science of Ukr. SSR, Kyiv, Inst. Mat., Preprint N 87.3, 1987, 27 p. (in Russian).
54. Yehorchenko I.A. On the group classification of equations for a complex vector potential, Group-theoretic investigations of the equations of mathematical physics, Acad. of Science of Ukr. SSR, Inst. Mathematics, Kyiv, 1985, 66-70 (in Russian).