Stanislav SPICHAK

Address:
Department of Applied Research
Institute of Mathematics
National Academy of Sciences of Ukraine
3 Tereshchenkivs'ka Street
01601 Kyiv-4
UKRAINE

Fax:
+ 380 (44) 235 20 10 (office)

E-mail: spichak@imath.kiev.ua

URL: http://www.imath.kiev.ua/~spichak/

Date of Birth: 22.03.1964 (Ulianovsk region, Russia)

Nationality: Ukraine

Academic Background:
Ph.D. in Math.: 1992, Institute of Mathematics, Kyiv (Supervisor Professor W.I. Fushchych)
M.Sc. in Math.: 1987, Moscow Physical Technical Insitute

Professional Experience:

1994-till now
Junior Researcher, Researcher, Senior Researcher at the Department of Applied Research of the Institute of Mathematics, Kyiv

1987-1990
Postgraduate Student, Institute of Mathematics, Kyiv (Supervisor Prof. W.I. Fushchych)

Marital Status: married, daughter (born 2011)

Other activities:
Organization of the First, Second, Third, Fourth, Fifth and Sixth International Conferences ``Symmetry in Nonlinear Mathematical Physics'' (Kyiv, Ukraine, 1995, 1997, 1999, 2001, 2003, 2005);
Associate Professor of Mathematics and Informatics, National Academy of Manadement, Kyiv (2002-2003).

AREA OF EXPERTISE:
Symmetry analysis of differential equations and applications, group theory, Lie algebras, exactly solvable systems

Referee:
Ukrainian Mathematical Journal

Reviewer
Mathematical Review
Mathematical Zenterblatt

Participation at the International Conferences and Schools:
International scientific conference dedicated to the 55th anniversary of the Faculty of Mathematics and Informatics (September 28-30, 2023, Chernivtsi, Ukraine)
International scientific conference dedicated to the 85th anniversary of M.P. Lenyuk (October 28-30, 2021, Chernivtsi, Ukraine)
16-th Conference ''Mathematics in Technical and Natural Sciences'' (September, 2017, 2019, Zakopane, Poland)
9th Workshop Group Analysis of Differential Equations and Integrable Systems (June 10-14, 2018, Larnaca, Cyprus)
International scientific conference dedicated to the 80th anniversary of M.P. Lenyuk (Chernivtsi, Ukraine, 2016)
International Workshop "Symmetry and Integrability of Equations of Mathematical Physics" (December, 2015, 2016, Kyiv, Ukraine)
7th Workshop Group Analysis of Differential Equations and Integrable Systems (June 15-19, 2014, Larnaca, Cyprus)
6th Workshop Group Analysis of Differential Equations and Integrable Systems (June 17-21, 2012, Protaras, Cyprus)
5th Workshop Group Analysis of Differential Equations and Integrable Systems (June 6-10, 2010, Protaras, Cyprus)
I-VIII International Conferences ''Symmetry in Nonlinear Mathematical Physics'' (Kyiv, Ukraine, 1995, 1997, 1999, 2001, 2003, 2005, 2007, 2009)
4th Workshop Group Analysis of Differential Equations and Integrable Systems (October 26-30, 2008, Protaras, Cyprus)
International Conference ''Some actual problems of modern mathematics and mathematical education'' (2008, Saint Petersburg, Russia)
International Conference ''Differential equations and related topics'' (May 21-26, 2007, Moscow, Russia)
Modern methods in physical and mathematical sciences (November, 2006, Orel, Russia)
VI International Scientific Conference named after Academician M. Kravchuk (Kyiv, Ukraine, 1997)
International Conference ''Integral Methods in Science and Engineering'' (June, 1996, Rovaniemi, Finland)
Algebraic and analytical methods in the theory of differential equations (November 14-19, 1996, Orel, Russia)
V International Scientific Conference named after Academician M. Kravchuk (Kyiv, Ukraine, 1996)

SUMMARY OF MAIN RESEARCH RESULTS

  1. The invariance of Dirac equations with respect to different representations of the Poincare algebra has been obtained. The explicit formulae have been built which connect solutions of Dirac and Maxwell equations. Furthermore, the Dirac equations are turned out to possess a supersymmetry. New nonlinearly second-order conformal invariant equations for a spinor field have been built.
  2. Lie and Q-conditional symmetry and exact solutions of local Wilson renormalization group equation have been calculated and some exact solutions of its have been found. Symmetry classification of the Kramers equation, the one-dimensional Fokker-Planck-Kolmogorov equation with arbitrary drift and diffusion coefficients has been fulfilled. For the Kramers equation conditional symmetry and some exact solutions were calculated.
  3. It was found that  the Maxwell equations have the conditional symmetries, which are nonlinear representations of the Poincare algebra.
  4. The new methods for the construction of Hermitian quasi-exactly and exactly solvable matrix Schrödinger operators on line have been developed. On the basis of them multiparameter families of Hermitian quasi-exactly and exactly solvable matrix Schrödinger models were constructed. Some examples of such models with square-integrable functions of corresponding space were found.
  5. The problem of group classification of quasi-linear elliptic type equations in two-dimensional space has been investigated. The list of all equations of this type is obtained, which admit semisimple Lie algebras of symmetry operators and Lie algebras of symmetry operators with non-trivial Levi decomposition. Also, the list of all equations of this type, which admit solvable Lie algebras of symmetry operators has been obtained.
  6. The problems of group classification were studied for nonlinear equations of Kolmogorov type, for different types of equations Asian option pricing equation. Some classes of exact solutions have been constructed, as well as fundamental solutions for linear equations.
  7. All non-equivalent realizations on the circle of finite-dimensional algebras with non-zero Levy factor were constructed in explicit form. Also, realizations of known solvable algebras (of dimension not higher than five) in the class of vector fields have been described, which are not limited by the requirement of analyticity.


PUBLICATIONS

  1. Spichak S.V. Classification of realizations of Lie algebras of vector fields on a circle, Ukrainian Mathematical Journal, 2022, V. 74, N 3, 389-399 (in Ukrainian).
  2. Kopas I.M., Spichak S.V., Stognii V.I. Group classification of one class of (2+1)-dimensional linear pricing equations for Asian options, Bukovinian Mathematical Journal, 2022, V. 10, N 2, 240-248 (in Ukrainian).
  3. Kopas I.M., Spichak S.V., Stognii V.I. Symmetric properties and exact solutions of the (2+1)-dimensional linear pricing equation of Asian options, Symmetry and integrability of equations in mathematical physics, Proceedings of Inst. Mathematics of National Akad. Science of Ukraine, Kiev, 2019, V. 16, N 1, 164-173 (in Ukrainian).
  4. Rassoha I.V., Serov M.I., Spichak S.V., Stognii V.I. Group classification of a class of generalized nonlinear Kolmogorov equations and exact solutions, AIP, Journal of Mathematical Physics, 59 071514 (2018), 23 pp., arXiv:1709.08914.
  5. Gorbunova O., Kopas I., Spichak S.V., Stognii V. Symmetric properties and exact solutions of the (2+1)-dimensional linear Asian option pricing equation, Modern problems of mechanics and mathematics, Proceedings of Institute of Applied Problems of Mechanics and Mathematics named Ya.S. Pidstryhach, NAS of Ukraine, Lviv, 2018, V. 3, 165-166 (in Ukrainian).
  6. Rassoha I.V., Serov M.I., Spichak S.V., Stognii V.I. Group classification of nonlinear equations of Kolmogorov type, Scientific Bulletin of the National Technical University of Ukraine "KPI", 2013, N 4, 88-93 (in Ukrainian).
  7. Spichak S.V. Preliminary classification of realizations of two-dimensional Lie algebras of vector fields on a circle, in Proceedings of 6th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 17-21, 2012, Protaras, Cyprus), University of Cyprus, Nicosia, 2013, 212-218.
  8. Spichak S.V., Stognii V.I., Kopas I.M. Symmetric analysis and exact solutions of the linear equation Kolmogorov, Scientific Bulletin of the National Technical University of Ukraine "KPI", 2011, N 4, 93-97 (in Ukrainian).
  9. Spichak S.V., On algebraic classification of Hermitian quasi-exactly solvable matrix Schrodinger operators on line, in Proceedings of 5th Workshop "Group Analysis of Differential Equations and Integrable Systems" (June 6-10, 2010, Protaras, Cyprus), University of Cyprus, Nicosia, 2011, 184-199.
  10. Lahno V.I., Spichak S.V. Group classification of quasi-linear elliptic type equations. II. Invariance under solvable Lie algebras, Ukrainian Mathematical Journal, 2011, V. 63, N 2, 200-215 (in Ukrainian).
  11. Nikitin A.G., Spichak S.V., Vedula Yu. S., Naumovets A.G. Symmetries and modelling functions for diffusion processes, J. Phys. D: Appl. Phys., 2009, V. 42, 055301, 12 pp.
  12. Lahno V.I., Spichak S.V., Quasi-linear elliptic type equations invariant under five-dimensional solvable Lie algebras, in Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (October 26-30, 2008, Protaras, Cyprus), University of Cyprus, Nicosia, 2009, 121-134.
  13. Lahno V.I., Spichak S.V. Group analysis of quasilinear equations of elliptic type with respect to solvable Lie algebras, Proceedings of International Conference "Some actual problems of modern mathematics and mathematical education" (May, 2008, Saint Petersburg, Russia), Russian State Pedagogical University, Saint Petersburg, 2008, 75-79 (in Russian).
  14. Lahno V.I., Spichak S.V. Group classification of quasi-linear elliptic type equations. I. Invariance under Lie algebras with nontrivial Levi decomposition, Ukrainian Mathematical Journal, 2007, V. 59, N 11, 1532-1545 (in Ukrainian).
  15. Spichak S.V. Group classification of quasi-linear elliptic type equations, in Proceedings of International Conference ``Differencial Equations and Related Topics'' (21-26 May, 2007, Moscow): Book of Abstracts. - Moscow: Moscow University Press, 2007. - 379 P.
  16. Spichak S.V. Preliminary group classification of general two-dimensional quasi-linear elliptic type equations, Symmetry and integrability of equations of mathematical physics, Inst. Mathematics of National Akad. Science of Ukraine, Kiev, 2006, V. 3, N 2, 284-292.  (pdf)
  17. Lahno V.I., Spichak S.V. Preliminary group classification of quasi-linear elliptic type equations, in Proceedings of International Conference ``Modern methods in physical-mathematical sciences'' (9-14 October, 2006, Orel), Editor A.G. Meshkov, Orel State university, 2006, V.1, 79-83 (in Russian).
  18. Lahno V.I., Spichak S.V., Stognii V.I. Symmetry analysis of evolution type equations, Moscow - Izhevsk, RCD, 2004, 392 p. (in Russian, revised and exented version).
  19. Spichak S.V., Invariance of Maxwell's Equations under Nonlinear Representations of Poincar\'e Algebra, in Proceedings of Fifth International Conference ``Symmetry in Nonlinear Mathematical Physics'' (23-29 June, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A. Yehorchenko, Proceedings of Institute of Mathematics, Kyiv, 2004, V.50, Part 2, 961-964 [pdf].
  20. Lahno V.I., Spichak S.V., Stognii V.I. Symmetry analysis of evolution type equations, Kyiv, Institute of Mathematics of NAS of Ukraine, 2002, 360 p. (in Ukrainian) (you can download here ps and pdf).
  21. Spichak S.V. On multi-parameter families of Hermitian exactly solvable matrix Schrödinger models, Symmetry in nonlinear mathematical physics, Part 1, 2, Proceedings of Inst. Mathematics of National Akad. Science of Ukraine (Kiev, 2001), 2002, V. 43, 688-690 (pdf).
  22. Abramenko A.O., Spichak S.V. On new classes of Hermitian exactly solvable matrix Schrödinger operators, Mat. Stud., 2001, V. 15, N 1, 44-56 (in Ukrainian).
  23. Abramenko A.O., Spichak S.V. Multiparameter families of Hermitian exactly solvable matrix Schrödinger models, Group and analytic methods in mathematical physics, Proceedings of Inst. Mathematics of National Akad. Science of Ukraine, Kiev, 2001, V. 36, 12-24 (in Ukrainian). (pdf)
  24. Spichak S.V., Stognii V.I. One-dimensional Fokker-Planck equation invariant under four- and six-parametrical group, Symmetry in nonlinear mathematical physics, Part 1, 2, Proceedings of the Conference of Inst. Mathematics of National Akad. Science of Ukraine, Kiev (1999), 2000, V. 30, Part 1, 204-209 (pdf).
  25. Spichak S.V., Stognii V.I. Symmetric classification of the one-dimensional Fokker-Planck-Kolmogorov equation with arbitrary drift and diffusion coefficients, Nonlinear oscillations, 1999, V. 2, N 3, 401-413 (in Russian).
  26. Spichak S.V. Quasi-exactly solvable 2x2 matrix Schrödinger models, Proceedings of the XXX Symposium on Mathematical Physics (Torun, 1998). Rep. Math. Phys., 1999, V. 44, no. 1-2, 215-220.
  27. Spichak S.V., Stognii V.I. Symmetry classification and exact solutions of the one-dimensional Fokker-Planck equation with arbitrary coefficients of drift and diffusion, J. Phys. A, 1999, V. 32, N 47, 8341-8353.
  28. Spichak S.V., Zhdanov R.Z. On algebraic classification of Hermitian quasi-exactly solvable matrix Schrödinger operators on line, J. Phys. A, 1999, V. 32, N 20, 3815-3831 (see math-ph/9812001).
  29. Spichak S.V., Stognii V.I. Symmetry classification and exact solutions of the Kramers equation, J. Math. Phys., 1998, V. 39, N 6, 3505-3510.
  30. Spichak S.V. Invariance of the Maxwell equations with respect to nonlinear representations of the Poincaré algebra, Symmetry and analytic methods in mathematical physics, Inst. Mathematics of National Akad. Science of Ukraine, Kiev, 1998, V. 19, 221-225  (in Russian). (pdf)
  31. Spichak S.V., Stogny V.I. Symmetry analysis of the Kramers equation, Rep. Math. Phys., 1997, V. 40, N 1, 125-130.
  32. Spichak S.V., Stognii V.I. Conditional symmetry and exact solutions of the Kramers equation, Symmetry in nonlinear mathematical physics, Vol. 1, 2 (Kiev), 1997, 450-454 (pdf).
  33. Spichak S.V. On the Poincaré-invariant second-order partial equations for a spinor field, J. Nonlinear Math. Phys., 1996, V. 3, no. 1-2, 156-159 (pdf).
  34. Shtelen W.M., Spichak S.V. Lie and Q-conditional symmetry and exact solutions of local Wilson renormalization group equation, Symmetry analysis of equations of mathematical physics, Acad. Sci. Ukraine, Inst. Math., Kiev, 1992, 50-54.
  35. Fushchich W.I., Shtelen W.M. and Spichak S.V. On the connection between solutions of Dirac and Maxwell equations, dual Poincaré invariance and superalgebras of invariance and solutions of nonlinear Dirac equations, J. Phys. A, 1991, V. 24, N 8, 1683-1698 (pdf).
  36. Fushchich V.I., Shtelen V.M. and Spichak S.V. On a connection between solutions of Dirac and Maxwell equations. Supersymmetry of the Dirac equation, Reports of Akad. Science of Ukrain SSR, Ser. A , 1990, V. 87, N 3, 36-40 (in Russian) (pdf).
  37. Spichak S.V., Vector representation of the Poincaré algebra and exact solution of the Dirac equation, Algebra-theoretic analysis of equations in mathematical physics (in Russian), Akad. of Science of Ukraine SSR, Institute of Mathematics, Kiev, 1990, 70-73.
  38. Spichak S.V. A new second-order conformally invariant equation for a spinor field, Symmetry and solutions of equations of mathematical physics, Akad. of Science of Ukrain. SSR, Inst. Mathematics, Kiev, 1989, 79-81 (in Russian).
  39. Shtelen V.M., Spichak S.V. On the invariance of the Dirac equation with respect to different representations of the Poincaré algebra, Symmetry and solutions of equations of mathematical physics, Akad. of Science of Ukrain. SSR, Inst. Mathematics, Kiev, 1989, 114-118 (in Russian).