Stanislav SPICHAK
Address:
Department
of Applied Research
Institute of Mathematics
National Academy of Sciences of Ukraine
3 Tereshchenkivs'ka Street
01601 Kyiv4
UKRAINE
Phone:
+380 (44) 234 63 22 (office)
Fax:
+ 380 (44) 235 20 10 (office)
Email: 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:
1994till now
Junior Researcher, Researcher, Senior Researcher at the
Department
of Applied Research of the Institute of Mathematics, Kyiv
19871990
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 (20022003).
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

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 secondorder conformal invariant equations for a spinor
field have been built.

Lie and Qconditional 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 onedimensional FokkerPlanckKolmogorov equation with
arbitrary drift and diffusion coefficients has been fulfilled. For the
Kramer’s equation conditional symmetry and some exact solutions were calculated.

It was found that the Maxwell equations have the conditional
symmetries, which are nonlinear representations of the Poincare algebra.

The new methods for the construction of Hermitian quasiexactly
and exactly solvable matrix Schrödinger operators on line have been
developed. On the basis of them multiparameter families of Hermitian quasiexactly
and exactly solvable matrix Schrödinger models were constructed. Some
examples of such models with squareintegrable functions of corresponding
space were found.
PUBLICATIONS

Lahno V.I., Spichak S.V. Group classification of quasilinear elliptic type equations.
I. Invariance under solvable Lie algebras, Ukrainian Mathematical Journal,
2011, V. 63, N 2, 200215 (in Ukrainian).

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.

Lahno V.I., Spichak S.V. Group classification of quasilinear elliptic type equations.
I. Invariance under Lie algebras with nontrivial Levi decomposition, Ukrainian Mathematical Journal,
2007, V. 59, N 11, 15321545 (in Ukrainian).

Spichak S.V. Group classification of quasilinear elliptic type equations, in Proceedings of International Conference ``Differencial Equations and Related Topics''
(2126 May, 2007, Moscow): Book of Abstracts.  Moscow: Moscow University Press, 2007. 
379 P.

Spichak S.V. Preliminary group classification of general twodimensional quasilinear 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, 284292. (pdf)

Lahno V.I., Spichak S.V. Preliminary group classification of quasilinear elliptic type equations, in Proceedings of International Conference ``Modern methods in physicalmathematical sciences''
(914 October, 2006, Orel), Editor A.G. Meshkov, Orel State university, 2006,
V.1, 7983 (in Russian).

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).

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''
(2329 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, 961964 [pdf].

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).

Spichak S.V. On multiparameter 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, 688690 (pdf).

Abramenko A.O., Spichak S.V. On new classes of Hermitian
exactly solvable matrix Schrödinger operators, Mat. Stud.,
2001, V. 15, N 1, 4456 (in Ukrainian).

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, 1224 (in
Ukrainian). (pdf)

Spichak S.V., Stognii V.I. Onedimensional FokkerPlanck
equation invariant under four and sixparametrical 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, 204209 (pdf).

Spichak S.V., Stognii V.I. Symmetric classification
of the onedimensional FokkerPlanckKolmogorov equation with arbitrary
drift and diffusion coefficients, Nonlinear oscillations, 1999,
V. 2, N 3, 401413 (in Russian).

Spichak S.V. Quasiexactly solvable 2x2 matrix Schrödinger
models, Proceedings of the XXX Symposium on Mathematical Physics (Torun,
1998). Rep. Math. Phys., 1999, V. 44, no. 12, 215220.

Spichak S.V., Stognii V.I. Symmetry classification
and exact solutions of the onedimensional FokkerPlanck equation with
arbitrary coefficients of drift and diffusion, J. Phys. A, 1999,
V. 32, N 47, 83418353.

Spichak S.V., Zhdanov R.Z. On algebraic classification
of Hermitian quasiexactly solvable matrix Schrödinger operators on
line, J. Phys. A, 1999, V. 32, N 20, 38153831 (see mathph/9812001).

Spichak S.V., Stognii V.I. Symmetry classification
and exact solutions of the Kramers equation, J. Math. Phys., 1998, V.
39, N 6, 35053510.

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, 221225 (in
Russian). (pdf)

Spichak S.V., Stogny V.I. Symmetry analysis of the
Kramers equation, Rep. Math. Phys., 1997, V. 40, N 1, 125130.

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, 450454 (pdf).

Spichak S.V. On the Poincaréinvariant secondorder
partial equations for a spinor field, J. Nonlinear Math. Phys.,
1996, V. 3, no. 12, 156159 (pdf).

Shtelen W.M., Spichak S.V. Lie and Qconditional symmetry
and exact solutions of local Wilson renormalization group equation, Symmetry
analysis of equations of mathematical physics, Acad. Sci. Ukraine, Inst.
Math., Kiev, 1992, 5054.

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, 16831698 (pdf).

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, 3640 (in Russian) (pdf).

Spichak S.V., Vector representation of the Poincaré
algebra and exact solution of the Dirac equation, Algebratheoretic
analysis of equations in mathematical physics (in Russian), Akad. of Science
of Ukraine SSR, Institute of Mathematics, Kiev, 1990, 7073.

Spichak S.V. A new secondorder 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, 7981 (in Russian).

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, 114118
(in Russian).