Seminars of the Department of Applied Research
of Institute of Mathematics of NASU
17.00, Tuesday/Thursday, room 208/216

March 21
Anatoly Nikitin,
Laplace-Runge-Lenz vector for a particle with arbitrary spin  

March 14
Iryna Yehorchenko,
Classification of wave equations with respect to reductions  

March 7
Oleksandr Pocheketa,
Group classification and exact solutions of generalized Burgers equations  

February 28
Olena Vaneeva,
Admissible transformations in group classification problems  

January 24
Sergiy Kovalenko,
Invariant solutions of boundary value problems  

January 17
Iryna Yehorchenko,
Compatibility of a system of D'alembert and Hamilton equations and its exact solutions  

January 10
Stanislav Spichak,
Realizations of two-dimensional Lie algebras of vector fields on a circle  

December 27, 2012
Maryna Nesterenko, S-expansions of three-dimensional Lie algebras  

December 20, 2012
Nataliya Shapoval (Taras Shevchenko Kyiv National University), Symmetries of linear ODEs  

December 13, 2012
Irina Yehorchenko, Classification of inequivalent reductions. Example of Schroedinger equation  

November 29, 2012
Anatoly Nikitin, Integrable Schroedinger-Pauli equations for neutral particles  

November 1, 2012
Igor Gap'yak (Taras Shevchenko Kyiv National University), Kinetic equations of systems of hard spheres and properties of their solutions  

October 11, 2012
Vasyl' Davydovych, Reaction-diffusion systems: Q-conditional symmetries, exact solutions and their properties  

October 4, 2012
Oksana Kuriksha, Group analysis of systems of equations of mathematical physics invariant with respect to low-dimensional Lie algebras and Poincare algebra  

September 13, 2012
Olexandr Pokutny, Periodical solutions of Schroedinger equation in Hilbert space  

September 6, 2012
Olexandr Pocheketa, Reduction operators of Burgers equation  

August 27, 2012
Vladislav Pukhnachev  (Institute of Hydrodynamics of SB RAS), Group-theoretical methods in convection problems  

June 7, 2012
Yuri Karadzhov, Classification of form-invariant Schroedinger equations  

May 31, 2012
Vasyl' Davydovych, Q-conditional symmetry of the first type of nonlinear reaction-diffusion systems with constant diffusivities.  

May 24, 2012
Anatoly Nikitin, Superintegrable quantum-mechanical systems with spin  

May 17, 2012
Nataliya Shapoval (Taras Shevchenko Kyiv National University), Jacobi multipliers and symmetries of ODEs  

April 26, 2012
Roman Popovych, Computation of point symmetry and equivalence groups using algebraic method  

April 19, 2012
Maryna Nesterenko, Classification and contractions of nilpotent Lie algebras  

April 12, 2012
Olena Vaneeva, Computation of admissible transformations in classes of PDEs  

March 13, 2012
Vyacheslav Boyko, Symmetries of systems of ODEs  

January 26, 2012
Roman Popovych, Groupoid of admissible transformations in classes of DEs  

January 19, 2012
Anatoly Nikitin, Exactly solvable problems of quantum mechanics  

December 22, 2011
Roman Popovych, Introduction to the method of moving frames  

October 13, 2011
Sergiy Kovalenko, Lie symmetries and exact solutions of a nonlinear BVP with free boundaries  
Olexandr Pocheketa, Group classification and reduction operators of generalized Burgers equations  

October 6, 2011
Yuri Karadzhov, Form-invariant systems of Schroedinger equations  

September 29, 2011
Yevgen Makedonskii (Taras Shevchenko Kyiv National University), Noncommutative bases of derivations module of polynomials ring  

September 22, 2011
Roman Popovych, Singular reduction modules  

September 15, 2011
Roman Popovych, Algebraic method of group classification  

June 23, 2011
Sergiy Kovalenko Lie symmetries and exact solutions of a class of (1+3)-dimensional BVP with free boundaries  

June 2, 2011
Irina Yehorchenko, Differential invariants and conditional symmetries  

May 26, 2011
Vyacheslav Boyko, Theorems on maximal dimension of invariance algebras of DEs  

March 24, 2011
Valeriy Stogniy (NTUU "KPI", Kyiv), Symmetry reductions and exact solutions of a nonlinear Kolmogorov-type equation  

February 24, 2011
Olena Vaneeva, Contractions in classes of differential equations  

February 17, 2011
Anatoly Nikitin, Contractions of representations of Lie algebras  

February 10, 2011
Maryna Nesterenko, Contractions of nilpotent Lie algebras  

February 03, 2011
Roman Popovych, Algebraic method of group classification  

November 25, 2010
Liliia Myroniuk (Lesya Ukrayinka Volyn State University), Exact solutions and their properties for multidimensional evolution equations  

November 18, 2010
Sergiy Kovalenko, Lie symmetries of one class of boundary-value problems for nonlinear heat equation  

November 11, 2010
Yuri Karadzhov, Simplest supersymmetrical model  

October 28, 2010
Vasyl' Davydovych, Q-conditional symmetries and exact solutions of the Lotka-Volterra system  

April 29, 2010
Roman Popovych, Conservation laws and normal forms of evolution equations  

March 25, 2010
Irina Yehorchenko, Differential invariants for transitive differential algebras  

March 18, 2010
Sergiy Kovalenko, Symmetry of boundary-value problems with free boundaries  

February 18, 2010
Vyacheslav Boyko, Algebraic approach to construction of differential invariants  

February 11, 2010
Stanislav Spichak, Symmetry of stochastic differential equations  

December 24, 2009
Irina Yehorchenko, Characterization of PDEs 

December 17, 2009
Roman Popovych, Generalized reduction operators of evolution equations 

December 10, 2009
Maryna Nesterenko, On orthogonal polynomials and simple Lie algebras 

December 03, 2009
Liliia Myroniuk (Lesya Ukrayinka Volyn State University), Symmetries and exact solutions of the generalized film equation 
Sergiy Maksymenko, Continuous shifts along orbits of vector fields 

November 19, 2009
Olena Vaneeva, Common errors in finding exact solutions of nonlinear PDEs 

November 12, 2009
Maryna Nesterenko, Computation with almost periodic functions 

October 29, 2009
Anatoly Nikitin, New integrable model for Dirac fermion 

October 22, 2009
Oleksander Omelyan (Department of Mathematics, Poltava Technical University), Symmetry properties of systems of nonlinear equations of parabolical type 

June 4, 2009
Roman Popovych, Conservation laws of evolution equations 
Abstract:
Well-known results on conservation laws of (1+1)-dimensional evolution equations are reviewed and new ones are presented. They concern restrictions on orders of conserved densities, forms of equations which have low-order conserved densities, conservation laws of linear (1+1)-dimensional evolution equations etc.

February 5, 2009
Sergiy Kovalenko, On exact solutions of (1+1)-dimensional nonlinear Stefan's boundary value problem 

January 29, 2009
Roman Popovych, Generalized Inonu-Wigner contractions 

January 15, 2009
Maryna Nesterenko, Contractions of the certain Lie algebra classes 

December 11, 2008
Oksana Kuriksha, On a model of electrodynamics 

December 4, 2008
Roman Popovych, Myths of nonclassical symmetry 
Abstract:
The notion of nonclassical symmetry (also called Q-conditional or, simply, conditional symmetry) was introduced by Bluman and Cole in 1969. In the past two decades, the theoretical background of nonclassical symmetries was intensively investigated and methods based on nonclassical symmetry were effectively applied to finding exact solutions of many partial differential equations arising in physics, biology, financial mathematics etc. Despite this long period of studying nonclassical symmetries and the encouraging results achieved in applications, a number of basic problems of this theory are still open. Moreover, the literature contains a variety of non-rigorous definitions of key notions in the field, as well as a large number of heuristic results on fundamental properties of nonclassical symmetries. These widely held beliefs and practices we call the ‘mythology of nonclassical symmetry’. To make sense of these myths and apply the underlying ideas correctly and unambiguously, a considerable amount of care is needed. Otherwise, certain contradictions and inaccurate statements may ensue. This talk is the result of joint work with Michael Kunzinger (University of Vienna). Different myths on nonclassical symmetries presented in the literature will be discussed. We will try to answer, in particular, the following questions.
• Is a nonclassical symmetry a Lie symmetry of the united system of the initial equation and the corresponding invariant surface condition? Can a nonclassical symmetry be assumed to be a conditional symmetry of the initial equation if the corresponding invariant surface condition is viewed as an additional constraint? Is nonclassical symmetry a kind of symmetry in general? Does there exist a more appropriate name for this notion?
• What is a rigorous definition of nonclassical symmetry for systems of differential equations? Can this definition be formulated as a straightforward extension of the definition of nonclassical symmetry for single partial differential equations to the case of systems?
• Is the factorization of the set of nonclassical symmetries of a differential equation with respect to the usual equivalence relation of nonclassical symmetries a trivial preliminary step of the procedure for finding this set? What is the correct way of partitioning this set for the factorization? How are difficulties in solving the determining equations for operators of nonclassical symmetries connected with the orders of the associated reduced equations?
All of the myths we analyze will be illustrated by nontrivial examples which underline the usefulness of a careful study of these questions.

September 18, 2008
Roman Popovych, Singular reduction operators in dimension two. 
Abstract:
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to first-order ODEs are are exhaustively described. As examples, properties of singular reduction operators of (1+1)-dimensional evolution and wave equations are studied. It is shown how to favourably enhance the derivation of nonclassical symmetries for this class by an in-depth study of the corresponding singular vector fields.

July 3, 2008
Maryna Nesterenko, Quasi-crystals and related functions 

June 26, 2008
Roman Popovych, Conservation laws of evolution equations 

June 17, 2008
Irina Yehorchenko, Classification of differential invariants with respect to subalgebras of Poincaré algebra 

June 12, 2008
Roman Popovych, Potential conservation laws (the continuation) 

June 5, 2008
Lyudmila Blazhko (Department of Mathematics, Poltava Technical University), Conformal invariance of quasilinear wave equations and conditional invariance of sine-Gordon equations 

May 29, 2007
Olga Alexandrova (Donbass State Academy of Building and Architectures, Makeevka), Symmetry analysis of stochastic differential Ito equations 

May 22, 2008
Roman Popovych, Potential Conservation Laws 

April 10, 2008
Roman Cherniha, Asymptotic Symmetries of PDEs 

March 27, 2008
Lyudmila Blazhko (Department of Mathematics, Poltava Technical University), Generation of Solutions for the sine-Gordon equation 

March 20, 2008
Yuri Karadzhov (Taras Shevchenko Kyiv National University, Ukraine), Preliminary Group Classification of a System of Two Evolution PDEs 

February 7, 2008
Maryna Nesterenko, Orbit-functions of semisimple Lie groups of the rank 3 

January 31, 2008
Maryna Nesterenko, Root system and weight system, Weyl group and affine Weyl group, fundamental region and grid on it 

January 17, 2008
Roman Popovych, Singular sets of reduction operators 

January 10, 2008
Olena Vaneeva, Group analysis of diffusion equations 

December 27, 2007
Roman Popovych, Reduction operators of linear parabolic equations 

December 20, 2007
Liliia Myroniuk (Lesya Ukrayinka Volyn State University), Exact solutions of the generalized Lotka-Volterra system with cross-diffusion 

December 13, 2007
Irina Yehorchenko, Utilization of Vessiot method to classes of PDE 

November 29, 2007
Irina Yehorchenko, Characterization of partial differential equations 

November 22, 2007
Maxim Pavlov (P.N. Lebedev Physical Institute, Moscow, Russia), On integration of Gibbons-Tsarev equation 

November 8, 2007
Nataliya Ivanova, Enhanced group analysis of diffusion-convection equations 

November 1, 2007
Bogdan Kochetov (V.N. Karazin Kharkiv National University), Symmetry analysis of the one-dimensional Klein-Gordon-Fock equation in spherical coordinates 

October 25, 2007
Oleksii Pliukhin, Q-conditional symmetries and exact solutions of systems of nonlinear reaction-diffusion equations 

October 18, 2007
Irina Yehorchenko, Relative invariants 

September 6, 2007
Olena Vaneeva, Group classification and nonclassical symmetries of reaction-diffusion equations 

June 14, 2007
Roman Popovych, Extended symmetry analysis of linear parabolic equations:
III. General potential symmetries and multiple dual Darboux transformations problems 
Abstract:
Extended symmetry analysis is performed for the class of linear (1+1)-dimensional second-order parabolic equations. The last talk from the series is devoted to general potential symmetries. Different criteria on existence of potential symmetries are proposed. The main tools of the investigation are the prolongation of equivalence transformations to the entire potential frame and multiple dual Darboux transformations.

June 11, 2007
Roman Popovych, Extended symmetry analysis of linear parabolic equations:
II. Local and potential conservation laws. Simplest potential symmetries. 
Abstract:
Extended symmetry analysis is performed for the class of linear (1+1)-dimensional second-order parabolic equations. The second talk from the planned series is devoted to conservation laws and simplest potential symmetries. It is proved that for any linear parabolic equation the space of characteristics associated with the local conservation laws can be identified with the solution space of the adjoint equation and any potential conserved vector is equivalent to a local one. Criterion on existence of simplest potential symmetries are found. The simplest potential symmetries of the linear heat equation are completely described. The dual Darboux transformations naturally arises as a powerful tool for the investigation of potential symmetries of the linear parabolic equations.

June 7, 2007
Roman Popovych, Extended symmetry analysis of linear parabolic equations:
I. Admissible transformations, normalized classes and the adjoint variational principle with application to group classification problems 
Abstract:
Extended symmetry analysis is performed for the class of linear (1+1)-dimensional second-order parabolic equations. The first talk from the planned series is devoted to admissible transformations and classical Lie symmetries. The admissible transformations in the class under consideration and its important subclasses (Kolmogorov equations, Fokker-Planck equations, different reduced forms) are completely described. The group classifications are given for different gauges of arbitrary elements (classical, Kolmogorov, Fokker-Planck ones). The classification results are revised with usage of admissible transformations, the notion of normalized classes of differential equations and the adjoint variational principle.

May 17, 2007 (16:00)
Olga Alexandrova (Donbass State Academy of Building and Architectures, Makeevka), Group Analysis of Stochastic Differential Ito Equations 

May 10, 2007
Nataliya Ivanova, Conservation laws and potential symmetries of linear parabolic equations 

April 26, 2007
Olena Vaneeva, Group classification of variable coefficient semilinear reaction-diffusion equations with a power source 

March 29, 2007
Vyacheslav Boyko, Invariants of triangular Lie algebras 

March 1, 2007
Stanislav Spichak, Symmetry classification of quasi-linear elliptic type equations with respect to five-dimensional solvable algebras 

February 22, 2007
Anatoly Nikitin, Contractions of Lorentz group representations and relativistic wave equations to Galilei group representations and, correspondingly, to equations which are invariant with respect to this group  

February 15, 2007
Nataliya Ivanova, Conservation laws of non-Lagrangian equations 

December 21, 2006
Roman Popovych, Generalization of Group Classification 

December 14, 2006
Maryna Nesterenko, Contractions and Realizations of Lie Algebras 

October 19, 2006
Oksana Gaponova, Second-order systems of ODEs invariant with respect to the real 3- and 4-dimensional Lie Algebras  

October 12, 2006
V.P. Karagodov, Unique solvability of thermoconvection problems of incompressible viscous fluid under boundary conditions of the second and third kinds and iteration method for their solvability 

July 27, 2006
Ilya I.Ryzhkov (Institute of Computational Modelling, Krasnoyarsk, Russia and Microgravity Research Center, Universite Libre de Bruxelles, Belgium), Group Analysis of the Convection Equations of a Binary Mixture 

June 8, 2006
Maryna Nesterenko, Contractions and Realizations of Lie Algebras  

May 25, 2006
Oleksii Plyukhin, Conditional Symmetries and Exact Solutions of a Reaction-diffusion-convection Equation 

May 11, 2006
Alexander Galkin (Department of Cybernetics, Kyiv National Taras Shevchenko University), Poincare Parasuperalgebra with Nontrivial Central Charges (the continuation) 

April 20, 2006
Alexander Galkin (Department of Cybernetics, Kyiv National Taras Shevchenko University), Poincare Parasuperalgebra with Nontrivial Central Charges 

April 13, 2006
Vyacheslav Boyko, Computation of Invariants of Lie Algebras by Means of Moving Frames 

March 16, 2006
Maryna Nesterenko, Realizations of Lie Algebras via Linear Algebra (the continuation) 

March 9, 2006
Maryna Nesterenko, Realizations of Lie Algebras via Linear Algebra 

March 2, 2006
Irina Yehorchenko, General Results on Conditional Symmetry for the Two-Dimensional Nonlinear Wave Equation 

February 23, 2006
Petro Holod (Department of Physical and Mathematical Sciences, National University of "Kyiv-Mohyla Academy"), Separation of variables in a finite class of integrable solitonic equations

January 26, 2006
Vyacheslav Boyko, Orbit functions on simple Lie group (review) 

December 22, 2005
Alexander Zhalij, Introduction into finite-gap integration theory

December 15, 2005
Roman Popovych, Reduction operators of (1+1)-dimensional second order linear parabolic equations 

December 8, 2005
Anatoly Nikitin, Exactly solvable problems for the Dirac equation 

December 1, 2005
Roman Popovych, On classification of reduction operators 

November 17, 2005
Stanislav Spichak, Preliminary group classification of the quasilinear two-dimensional elliptic equations 

November 10, 2005
Vyacheslav Boyko and Roman Popovych, Invariants of Lie algebras 

October 6, 2005
Maryna Nesterenko, Contractions of representations of Lie algebras 

September 29, 2005
Maryna Nesterenko, Contractions of low-dimensional Lie algebras 

September 22, 2005
Olena Vaneeva, Classification of nonclassical symmetry operators of the nonlinear filtration equation  

September 15, 2005
Volodymyr Tkachuk (Ivan Franko National University of L'viv), Supersymmetry and exact-solvable problems in quantum mechanics

August 22, 2005
Kurt W. Just (Department of Physics, University of Arizona, USA), Abelian Higgs Model in Quantum Induction

August 4, 2005
Olena Vaneeva, Potential nonclassical symmetries and exact solutions of fast diffusion equation

July 21, 2005
Jamil Daboul (Ben Gurion University of the Negev, Beer Sheva, Israel), Symmetries and solutions of a pseudo-diffusion equation

June 30, 2005
Victor Robuk (Joint Institute for Nuclear Research, Dubna, RUSSIA and Electro-Physical Scientific & Technical Centre of NAS of Ukraine, Kharkiv, UKRAINE), Some remarks to the Wahlquist-Estabrook method on the example of the linear heat equation

June 2, 2005
Roman Popovych, Solutions of diffusion equations (review)

May 26, 2005
Maryna Nesterenko, Contractions of Lie groups and Lie algebras  (the continuation)

May 19, 2005
Maryna Nesterenko, Contractions of Lie groups and Lie algebras

May 12, 2005
Irina Yehorchenko, Classification of types of conditional and partial symmetries

April 21, 2005
Anatoly Nikitin, Vector covariants of Galilei group

April 14, 2005
Alexander Zhalij, Superintegrability

March 31, 2005
Petro M. Denysenko (Kirovograd State Technical University), Optimal algorithm for Lantsosh tau-method

March 3, 2005
Igor Bratchun, On nonlinear model which admits Galilei parasupergroup

February 24, 2005
Tetyana Barannyk (Poltava State Pedagogical University), Galilei-invariant systems of diffusion equations

February 21, 2005
Roman Popovych, Q-conditional (nonclassical) symmetries of PDEs

February 17, 2005
Tamara Zhadan (Department of Mathematics, Poltava Technical University), Symmetry classification of nonlinear systems of diffusion-convection equations

February 10, 2005
Roman Popovych, Normalized classes of nonlinear Schrodinger equations (the continuation)

February 3, 2005
Roman Popovych, Normalized classes of nonlinear Schrodinger equations

January 20, 2005
Olga Alexandrova (Donbass State Academy of Building and Architectures, Makeevka), Symmetries of linear stochastic equations

January 13, 2005
Anatoly Nikitin, Relativistic particle with arbitrary half integer spin interacting with Coulomb field

December 23, 2004
Vyacheslav Boyko, Symmetry and integration of ODE

December 2, 2004
Roman Popovych, Conservation laws

November 25, 2004
Igor Bratchun, Nonlinear Galilei supersymmetric models

November 18, 2004
Maryna Nesterenko, On classification of real Lie algebras (approaches and methods)

November 11, 2004
Nataliya Ichans'ka (Department of Mathematics, Poltava Technical University), Lie and Q-conditional symmetries of evolution PDEs

October 21, 2004
Victor Lehenkyi, Group-theoretical aspects of parametric reduction of ODEs

October 14, 2004
Roman Popovych, Equivalence in classes of differential equations

October 7, 2004
Alexander Galkin (Department of Cybernetics, Kyiv National Taras Shevchenko University), Poincare parasuperalgebra  and equations for particles with higher spins

September 30, 2004
Aleksej Borovskikh (Department of Mechanics and Mathematics, Moscow State University), Eikonal equation in inhomogeneous medium

September 23, 2004
Irina Yehorchenko, Differential invariants

September 16, 2004
Nataliya Ivanova, Classification problems for diffusion-convection equations and Schrodinger equations

September 9, 2004
Igor Bratchun, (Para)supersymmetric models in quantum physisc

September 2, 2004
Christodoulos Sophocleous (Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus), Potential symmetries of system of diffusion equations

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