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)

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  • 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
    Nonlinear Mathematical Physics" (in PDF format). Please contact us if you have any difficulties with downloading the files (

    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)

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