Stanislav SPICHAK

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

Phone:
+380 (44) 234 63 22 (office)

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
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: single

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, exactly solvable systems
 

HOBBY:

I am keen on mountain tourism.
 

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 and the one-dimensional Fokker-Planck-Kolmogorov equation with arbitrary drift and diffusion coefficients has been fulfilled. For the Kramerís 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.


PUBLICATIONS

  1. Lahno V.I., Spichak S.V. Group classification of quasi-linear elliptic type equations. I. Invariance under solvable Lie algebras, Ukrainian Mathematical Journal, 2011, V. 63, N 2, 200-215 (in Ukrainian).
  2. 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.
  3. 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).
  4. 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.
  5. 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)
  6. 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).
  7. 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).
  8. 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].
  9. 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).
  10. 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).
  11. 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).
  12. 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)
  13. 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).
  14. 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).
  15. 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.
  16. 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.
  17. 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).
  18. 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.
  19. 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)
  20. Spichak S.V., Stogny V.I. Symmetry analysis of the Kramers equation, Rep. Math. Phys., 1997, V. 40, N 1, 125-130.
  21. 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).
  22. 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).
  23. 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.
  24. 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).
  25. 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).
  26. 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.
  27. 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).
  28. 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).