## The Proceedings of SNMP'99

are published as Part 1 (pages 1-264) and Part 2 (pages 265-552) of Volume 30 of Proceedings of Institute of Mathematics
NAS of Ukraine, Editors A.G. Nikitin and V.M. Boyko, Kyiv, Institute of Mathematics, 2000.

ISBN 966-02-1444-8 (general)
ISBN 966-02-1401-4  (for Part 1)
ISBN 966-02-1402-2  (for Part 2)

You can download the contents of both parts in PostScript and PDF formats:

• PostScript File
• PDF File

• These Proceedings are papers of the third conference in the series "Symmetry in Nonlinear Mathematical Physics"

!!!!! You can download both parts of Proceedings: pdf (8,56 Mb) or djvu (4,1 Mb)

We present the full list of articles, which are published in Proceedings of Third International Conference "Symmetry in

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)

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)

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)

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. 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)

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)

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)

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)

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