ISBN 966-02-1444-8 (general)
ISBN 966-02-1401-4 (for Part 1)
ISBN 966-02-1402-2 (for Part 2)
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These Proceedings are papers of the third conference in the series Symmetry
in Nonlinear Mathematical Physics
see http://www.imath.kiev.ua/~appmath/conf.html
!!!!! You can download both parts of Proceedings: pdf (8,56 Mb)
We present the full list of articles, which are published in Proceedings
of Third International Conference "Symmetry in
Nonlinear Mathematical Physics" (in PDF format).
Part 1
NIKITIN A.G., Preface (pages 5-5)
List of Participants (pages 8-11)
Symmetry of Differential Equations
HARRISON B.K., Matrix Methods of Searching for Lax Pairs and a Paper by Estevez (pages 17-24)
BERKOVICH L.M., Transformations of Ordinary Differential Equations: Local and Nonlocal Symmetries (pages 25-34)
MESHKOV A.G., Computer Package for Investigation of the Complete Integrability (pages 35-46)
NIKITIN A.G., WILTSHIRE R.J., Symmetries of Systems of Nonlinear Reaction-Diffusion Equations (pages 47-59)
ABD-EL-MALEK M.B., EL-AWADI I.A. and EL-MANSI S.M.A., Electro-Static Potential Between Two Conducting Cylinders via the Group Method Approach (pages 60-67)
BALAKHNEV M.Ju., KULEMIN I.V. and MESHKOV A.G., New Evolution Completely Integrable System (pages 68-72)
BARANNYK A.F. and YURYK I.I, Separation of Variables and Construction of Exact Solutions of Nonlinear Wave Equations (pages 73-82)
BARANNYK L.F., On Exact Solutions of the Nonlinear Heat Conduction Equation with Source (pages 83-89)
BERKOVICH L.M. and ORLOVA I.S., The Exact Linearization of Some Classes of Ordinary Differential Equations for Order $n> 2$ (pages 90-98)
BOYKO V., On the Galilei Invariance of the Continuity Equation (pages 99-102)
FEDORCHUK V.M., FEDORCHUK I.M. and FEDORCHUK V.I., On Symmetry Reduction of the Five-Dimensional Dirac Equation (pages 103-108)
FEDORCHUK V.M. and LEIBOV O., On Symmetry Reduction and Some Exact Solutions of the Multidimensional Born--Infeld Equation (pages 109-115)
FUJII K., Nonlinear Integrable Models with Higher d'Alembertian Operator in Any Dimension (pages 116-119)
HU X.-B. and LOU S.-Y., Nonlocal Symmetries of Nonlinear Integrable Models (pages 120-126)
KHOMCHENKO L.V., Oscillation of Solutions of Ordinary
Differential Equations Systems Generated by Finite-Dimensional
Group Algebra (pages 127-130)
KUSYUMOV A., About Symmetries of Exterior Differential Equations, Appropriated to a System of Quasilinear Differential Equations of the First Order (pages 131-136)
KUZMENKO A., Construction of Invariants for a System of Differential Equations in the $n+2m$-Dimensional Space (pages 137-140)
LAHNO V. and ONYSHCHENKO A., The Ovsjannikov's Theorem on Group Classification of a Linear Hyperbolic Type Partial Differential Equation Revisited (pages 141-145)
LAHNO V. and ZHDANOV R.Z., Towards a Classification of Realizations of the Euclid Algebra $e(3)$ (pages 146-150)
LUTFULLIN M., Realizations of the Euclidean Algebra within the Class of Complex Lie Vector Fields (pages 151-156)
LEHENKYI V., The Integrability of Some Underdetermined Systems (pages 157-164)
MAGDA O., The Group Classification of Nonlinear Wave Equations Invariant under Two-Dimensional Lie Algebras (pages 165-169)
MU\~NOZ MASQU\'E J. and POZO CORONADO L.M., Hamiltonian Formulation and Order Reduction for Nonlinear Splines in the Euclidean 3-Space (pages 170-176)
PANCHAK O., A Class of Non-Lie Solutions for a Non-linear d'Alembert Equation (pages 177-179)
POPOVYCH H.V., On $SO(3)$-Partially Invariant Solutions of the Euler Equations (pages 180-183)
POPOVYCH R.O., Equivalence of $Q$-Conditional Symmetries Under Group of Local Transformation (pages 184-189)
POPOVYCH V.O., Lie Submodels of Rank 1 for the MHD Equations (pages 190-195)
SERGYEYEV A., On Local Time-Dependent Symmetries of Integrable Evolution Equations (pages 196-203)
SPICHAK S. and STOGNII V., One-Dimensional Fokker--Planck Equation Invariant under Four- and Six-Parametrical Group (pages 204-209)
TAJIRI M. and ARAI T., Periodic Soliton Solutions to the Davey--Stewartson Equation (pages 210-217)
TSYFRA I., Symmetries and Reductions of Partial Differential Equations (pages 218-222)
VASSILEV V.M. and DJONDJOROV P.A., Symmetry Groups and Conservation Laws in Structural Mechanics (pages 223-231)
VLADIMIROV V.A., Modelling System for Relaxing Media. Symmetry, Restrictions and Attractive Features of Invariant Solutions (pages 232-238)
VLADIMIROV V.A. and SKURATIVSKY S.I., On Invariant Wave Patterns in Non-Local Model of Structured Media (pages 239-244)
YEHORCHENKO I., On Symmetry of a Class of First Order PDEs Equations (pages 245-248)
ZHALIJ A., On Some New Classes of Separable Fokker--Planck Equations (pages 249-254)
ZHDANOV R.Z., Higher Conditional Symmetries
and Reduction of Initial Value Problems for Nonlinear Evolution Equations
(pages 255-263)
Part 2
q-Algebras and Quantum Groups
BECKERS J., On Nonlinear Deformations of Lie Algebras and their Applications in Quantum Physics (pages 275-279)
HAVL\'{I}\v CEK M., PO\v STA~S. and KLIMYK A.U., Representations of the $q$-Deformed Algebra ${\mathrm{so}}_{q}(2,1)$ (pages 280-287)
QUESNE C. and VANSTEENKISTE N., $C_\lambda$-Extended Oscillator Algebras: Theory and Applications to (Variants of) Supersymmetric Quantum Mechanics (pages 288-297)
BURBAN I.M., Some Problems of Quantum Group Gauge Field Theory (pages 298-303)
GAVRILIK A.M., The Use of Quantum Algebras in Quantum Gravity (pages 304-309)
GAVRILIK A.M. and IORGOV N.Z., On the Casimir Elements of $q$-Algebras ${U'_q({\rm so}_n)}$ and Their Eigenvalues in Representations (pages 310-314)
Algebras and Groups: Developments and Applications
KLINK W.H., Discrete Subgroups of the Poincar\'{e} Group (pages 317-323)
ABRAMENKO A., Matrix Realizations of Four-Dimensional Lie Algebras and Corresponding Invariant Spases (pages 324-329)
BONDARENKO V.M., Operators on $(A,\ast)$-Spaces and Linear Classification Problems (pages 330-332)
GALKIN A.V., Poincar\'e Parasuperalgebra with Central Charges (pages 333-340)
KALUTSKII S., On $*$-Wild Algebras (pages 341-342)
NAZARENKO A., Canonical Realization of the Poincar\'e Algebra for a Relativistic System of Charged Particles Plus Electromagnetic Field (pages 343-349)
OHNUKI Y., Irreducible Representations of the Dirac Algebra for a System Constrained on a Manifold Diffeomorphic to $S^{D}$ (pages 350-356)
PAVLENKO H. and PIRYATINSKA A., On Generalization of the Cuntz Algebras (pages 357-363)
POPOVYCH S.V. and MAISTRENKO T.Yu., $C^*$-Algebras Associated with Quadratic Dynamical System (pages 364-370)
Related Problems of Mathematical Physics
SHKIL M.I., On Asymptotic Decompositions for Solutions
of Systems of Differential Equations in the Case of Multiple
Roots of the Characteristic Equation (pages
373-381)
SHKIL M.I. and SAMUSENKO P.F., On Asymptotic Formulae for Solutions of Differential Equations with Summable Coefficients (pages 382-386)
FILCHAKOVA V.P., PP-Test for Integrability of Some Evolution Differential Equations (pages 387-391)
KONDAKOVA S., Asymptotic Integration of System of the Differential Equations of Third Order (pages 392-400)
KOROSTIL A.M., On Hyperelliptic Solutions of Spectral Problem for the Two-Dimensional Schr\"odinger Equation (pages 401-405)
SAMOYLENKO V.Hr., SIDORENKO Yu.M., BUONANNO L. and MATARAZZO G., Explicit Solutions of Nonlinear Evolution Equations via Nonlocal Reductions Approach (pages 406-410)
ZHUKOVSKY A.N. and KARAGODOV V.P., Exact Solutions of the Inhomogeneous Problems for Polyparabolic Operator (pages 411-416)
Symmetry in Physics and Other Natural Sciences
BINZ E. and SCHEMPP W., A Unitary Parallel Filter Bank Approach to Magnetic Resonance Tomography (pages 419-428)
GIELERAK~R. and \L UGIEWICZ P., Models of Covariant Quantum Theories of Extended Objects from Generalized Random Fields (pages 429-439)
GOLDIN G.A., Generalized Gauge Invariants for Certain Nonlinear Schr\"odinger Equations (pages 440-446)
GUHR T., Supersymmetry and Supergroups in Stochastic Quantum Physics (pages 447-455)
SHIMA K., Nonlinear Symmetry and Unity of Spacetime and Matter (pages 456-464)
ZAJTZ A., On the Global Conjugacy of Smooth Flows (pages 465-472)
DUVIRYAK A., Classical Mechanics of Relativistic Particle with Colour (pages 473-480)
FRAPPAT L., SCIARRINO A. and SORBA P., Crystal Basis Model of the Genetic Code: Structure and Consequences (pages 481-488)
GOLOVNIA R.M., On a Class of Equations for Paticles with Arbitrary Spin (pages 489-492)
KUCHERYAVY V.I., Symmetries, their Breaking and Anomalies in the Self-Consistent Renormalization. Discrete Symmetry Shadow in Chiral Anamalies (pages 493-500)
KUZMENKO T.Yu., Quantum Mechanism of Generation of the $SU(N)$ Gauge Fields (pages 501-506)
PAVLYUK A., Symmetric Properties of First-Order Equations of Motion for $N=2$ Super Yang--Mills Theory (pages 507-509)
ROYCHOUDHURY R., Quasipotential Approach to Solitary Wave Solutions in Nonlinear Plasma (pages 510-515)
SHPYTKO V., Weyl-Type Quantization Rules and $N$-Particle Canonical Realization of the Poincar\'e Algebra in the Two-Dimensional Space-Time (pages 516-523)
SKRYPNYK T., Quantum Integrability of the Generalized Eulers Top with Symmetries (pages 524-529)
SVIRINA L.P., Symmetry-Breaking Bifurcations in a Single-Mode Class-A Gas Laser (pages 530-536)
TRETYNYK V., On Exact Foldy--Wouthuysen Transformation of Bozons in an Electromagnetic Field and Reduction of Kemmer--Duffin--Petiau Equation (pages 537-543)
YAREMKO Yu., The Tangent Groups of a Lie Group and Gauge Invariance in Lagrangian Dynamics (pages 544-550)
NIKITIN A.G., Conclusion (pages 551-551)