The Proceedings of Fourth International Conference 
"Symmetry in Nonlinear Mathematical Physics"

are published as Part 1 (pages 1-392) and Part 2 (pages 393-784) of Volume 43 of Proceedings of Institute of Mathematics of NAS of Ukraine,
Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych, Kyiv, Institute of Mathematics, 2002.

ISBN 966-02-2486-9 (general)
ISBN 966-02-2487-7  (for Part 1)
ISBN 966-02-2488-5  (for Part 2)

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

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We present the full list of articles, which are published in Proceedings of Fourth 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 8-12)

SAMOILENKO A.M., Mykhailo Vasyl’ovych Ostrohrads’kyi (pages 17-24)

Symmetry of Differential Equations

HARRISON B.K., An Old Problem Newly Treated with Differential Forms: When and How Can the Equation $y'' = f(x,y,y)'$ Be Linearized? (pages 27-35)

BINDU P.S. and LAKSHMANAN M., Symmetries and Integrability Properties of Generalized Fisher Type Nonlinear Diffusion Equation (pages 36-48)

ABD-EL-MALEK M.B., BADRAN N.A. and HASSAN H.S., Solution of the Rayleigh Problem for a Power Law Non-Newtonian Conducting Fluid via Group Method (pages 49-56)

ABD-EL-MALEK M.B., BADRAN N.A.and HASSAN H.S., Using Group Theoretic Method to Solve Multi-Dimensional Diffusion Equation (pages 57-64)

AMDJADI F., Hopf Bifurcations in Problems with O(2) Symmetry: Canonical Coordinates Transformation (pages 65-71)

ANDREYTSEV A., Classiffcation of Systems of Nonlinear Evolution Equations Admitting Higher-Order Conditional Symmetries (pages 72-79)

BARANNYK T., Symmetry and Exact Solutions for Systems of Nonlinear Reaction-Diffusion Equations (pages 80-85)

BASARAB-HORWATH P. and LAHNO V., Group Classiffcation of Nonlinear Partial Differential Equations: a New Approach to Resolving the Problem (pages 86-92)

BURDE G.I., Expanded Lie Group Transformations and Similarity Reductions of Differential Equations (pages 93-101)

CHERNIHA R. and SEROV M., Nonlinear Diffusion-Convection Systems: Lie and Q-Conditional Symmetries (pages 102-110)

CHUGUNOV V.A., GRAY J.M.N.T. and HUTTER K., Some Invariant Solutions of the Savage-Hutter Model for Granular Avalanches (pages 111-119)

CICOGNA G., Symmetric Sets of Solutions to Differential Problems (pages 120-127)

COTSAKIS S. and LEACH P.G.L., Symmetries, Singularities and Integrability in Nonlinear Mathematical Physics and Cosmology (pages 128-135)

FEDORCHUK I.M., On New Exact Solutions of the Eikonal Equation (pages 136-139)

FEDORCHUK V.M. and FEDORCHUK V.I., On Differential Invariants of First- and Second-Order of the Splitting Subgroups of the Generalized Poincare Group P(1,4) (pages 140-144)

FEDORCHUK V.I., On Differential Equations of First- and Second-Order in the Space $M(1,3) \times R(u)$ with Nontrivial Symmetry Groups (pages 145-148)

IVANOVA N., Symmetry of Nonlinear Schr\"odinger Equations with Harmonic Oscillator Type Potential (pages 149-150)

van der KAMP P.H., The Use of p-adic Numbers in Calculating Symmetries of Evolution Equations (pages 151-155)

KOTEL’NIKOV G., Method of Replacing the Variables for Generalized Symmetry of D’Alembert Equation (pages 156-161)

LAHNO H.O. and SMALIJ V.F., Subgroups of Extended Poincare Group and New Exact Solutions of Maxwell Equations (pages 162-166)

MAGDA O., Invariance of Quasilinear Equations of Hyperbolic Type with Respect to Three-Dimensional Lie Algebras (pages 167-170)

MISKINIS P., New Exact Solutions of Khokhlov-Zabolotskaya-Kuznetsov Equation (pages 171-177)

POPOVYCH H.V., Lie, Partially Invariant, and Nonclassical Submodels of Euler Equations (pages 178-183)

POPOVYCH R.O. and BOYKO V.M., Differential Invariants and Application to Riccati-Type Systems (pages 184-193)

PROKHOROVA M.F., Heat Equation on Riemann Manifolds: Morphisms and Factorization to Smaller Dimension (pages 194-200)

REYES E.G., The Soliton Content of the Camassa-Holm and Hunter-Saxton Equations (pages 201-208)

SERGYEYEV A. and SANDERS J.A., The Complete Set of Generalized Symmetries for the Calogero-Degasperis-Ibragimov-Shabat Equation (pages 209-214)

SHEFTEL M.B., Method of Group Foliation and Non-Invariant Solutions of Invariant Equations (pages 215-224)

TARANOV V., The Most Symmetric Drift Waves (pages 225-228)

TSYFRA I.M., Conditional Symmetry Reduction and Invariant Solutions of Nonlinear Wave Equations (pages 229-233)

VLADIMIROV V. and SKURATIVSKII S., On the Localized Invariant Traveling Wave Solutions in Relaxing Hydrodynamic-Type Model (pages 234-239)

VOLKMANN J., SUDLAND N., SCHMID R., ENGELMANN J. and BAUMANN G., Symmetry Analysis of the Doebner-Goldin Equations (pages 240-251)

VOROBYOVA A., Transformation of Scientific System of Knowledge in Educational: Symmetry Analysis of Equations of Mathematical Physics (pages 252-255)

YEHORCHENKO I., Differential Invariants and Construction of Conditionally Invariant Equations (pages 256-262)

ZAWISTOWSKI Z.J., Symmetries of Integro-Differential Equations (pages 263-270)

Solitons and Integrability

BELOKOLOS E.D., Spectra of the Schr\"odinger Operators with Finite-Gap Potentials and Integrable Systems (pages 273-280)

CHOU K.S. and QU C.Z., Integrable Equations and Motions of Plane Curves (pages 281-290)

ANDERS I., Asymptotics of the Coupled Solutions of the Modified Kadomtsev-Petviashvili Equation (pages 291-295)

BERKELA Yu., Exact Solutions of Matrix Generalizations of Some Integrable Systems (pages 296-301)

DUBROVSKY V.G., FORMUSATIK I.B. and LISITSYN Ya.V., New Exact Solutions of Some Two-Dimensional Integrable Nonlinear Equations via $\overline{\partial}$.-Dressing Method (pages 302-313)

HARNAD J., ZHEDANOV A. and YERMOLAYEVA O., R-Matrix Approach to the Krall-Sheffer Problem (pages 314-320)

HVOZDOVA Ye., On Integrability of Some Nonlinear Model with Variable Separant (pages 321-322)

FIORAVANTI D., Aspects of Symmetry in Sine-Gordon Theory (pages 323-331)

LI Y., Integrable Structures for 2D Euler Equations of Incompressible Inviscid Fluids (pages 332-338)

OKSYUK G., High-Frequency Absorption by a Soliton Gas in One-Dimensional Magnet (pages 339-343)

PARKER A.and DYE J.M., Boussineq-Type Equations and “Switching” Solitons (pages 344-351)

SIDORENKO Yu.M., Transformation Operators for Integrable Hierarchies with Additional Reductions (pages 352-357)

SKRYPNIK W., On Integrable Quantum System of Particles with Chern-Simons Interaction (pages 358-363)

SKRYPNYK T.V., Integrable Hamiltonian Systems via Quasigraded Lie Algebras (pages 364-371)

SVININ A.K., nth Discrete KP Hierarchy (pages 372-376)

TODA K., The Construction of Alternative Modified KdV Equation in (2 +1) Dimensions (pages 377-383)

VAKHNENKO V.O. and PARKES E.J., A Novel Nonlinear Evolution Equation Integrable by the Inverse Scattering Method (pages 384-391)

Part 2

Algebras,Groups and Representation Theory

BECKERS J. and DEBERGH N., On the Heisenberg-Lie Algebra and Some Non-Hermitian Operators in Oscillatorlike Developments (pages 403-406)

KLIMYK A.U., On Classiffcation of Irreducible Representations of $q$-Deformed Algebra $U'_q (so_n)$ Related to Quantum Gravity (pages 407-418)

ARZHANTSEV I.V., Invariant Differential Operators and Representations with Spherical Orbits (pages 419-424)

BONDARENKO A. and POPOVYCH S., $C^*$-Algebras Associated with ${\mathcal F}_{2^n}$ Zero Schwarzian Unimodal Mappings (pages 425-431)

DEBERGH N. and STANCU Fl., The Lipkin-Meshkov-Glick Model and its Deformations through Polynomial Algebras (pages 432-438)

DUPLIJ S., Ternary Hopf Algebras (pages 439-448)

IORGOV N., On the Center of $q$-Deformed Algebra $U'_q(so_3$ Related to Quantum Gravity at $q$ a Root of 1 (pages 449-455)

JORGENSEN P.E.T., PROSKURIN D.P. and SAMOILENKO Yu.S., Generalized Canonical Commutation Relations: Representations and Stability of Universal Enveloping $C^*$-Algebra (pages 456-460)

KRUGLYAK S.A. and KYRYCHENKO A.A., On Four Orthogonal Projections that Satisfy the Linear Relation $\alpha_1 P_1 + \alpha_2 P_2 +\alpha_3 P_3 +\alpha_4 P_4 = I$, $\alpha_i>0$ (pages 461-465)

LUTFULLIN M.W. and POPOVYCH R.O., Realizations of Real 4-Dimensional Solvable Decomposable Lie Algebras (pages 466-468)

MAISTRENKO T.Yu., Positive Conjugacy for Simple Dynamical Systems (pages 469-473)

NESTERENKO M.O. and BOYKO V.M., Realizations of Indecomposable Solvable 4-Dimensional Real Lie Algebras (pages 474-477)

PALEV T.D., STOILOVA N.I. and VAN der JEUGT J., Jacobson Generators of (Quantum) $sl(n +1|m)$. Related Statistics (pages 478-485)

POPOVA N., On One Algebra of Temperley-LiebType (pages 486-489)

STRELETS A.V., On Involutions which Preserve Natural Filtration (pages 490-494)


NIEDERLE J.and NIKITIN A.G., Extended SUSY with Central Charges in Quantum Mechanics (pages 497-507)

PLYUSHCHAY M. and KLISHEVICH S., Nonlinear Supersymmetry (pages 508-519)

SAMSONOV B.F., Time-Dependent Supersymmetry and Parasupersymmetry in Quantum Mechanics (pages 520-529)

SHIMA K., Geometry of Nonlinear Supersymmetry in Curved Spacetime and Unity of Nature (pages 530-539)

GAVRILIK A.M., Quantum Algebras, Particle Phenomenology, and (Quasi)Supersymmetry (pages 540-547)

RAUSCH de TRAUBENBERG M. and SLUPINSKI M.J., Fractional Supersymmetry and F-fold Lie Superalgebras (pages 548-554)

Symmetry in Physics

KELLER J., General Relativity as a Symmetry of a Unified Space-Time-Action Geometrical Space (pages 557-568)

KLINK W.H., Point Form Relativistic Quantum Mechanics and an Algebraic Formulation of Electron Scattering (pages 569-576)

SCHMID R. and SUN Q., Relativity without the First Postulate (pages 577-588)

BEDRIJ O., New Relationships and Measurements for Gravity Physics (pages 589-601)

BURBAN I.M., D-branes, B Fields and Deformation Quantization (pages 602-608)

CASAHORRAN J., The Euclidean Propagator in Quantum Models with Non-Equivalent Instantons (pages 609-615)

GALKIN A., Equation for Particles of Spin $\frac 32$ with Anomalous Interaction (pages 616-622)

GLAZUNOV N., Mirror Symmetry: Algebraic Geometric and Lagrangian Fibrations Aspects (pages 623-628)

KUCHERYAVY V.I., Symmetries and Dynamical Symmetry Breaking of General n-Dimensional Self-Consistently Renormalized Spinor Diangles (pages 629-640)

NAON C. and SALVAY M., On a CFT Prediction in the Sine-Gordon Model (pages 641-644)

NASIRI S. and SAFARI H., A Symmetric Treatment of Damped Harmonic Oscillator in Extended Phase Space (pages 645-651)

NAZARENKO A., Canonical Realization of Poincare Algebra: from Field Theory to Direct-Interaction Theory (pages 652-658)

NURMAGAMBETOV A.J., Towards Uniform T-Duality Rules (pages 659-662)

PAVLYUK A., First Order Equations of Motion from Breaking of Super Self-Duality (pages 663-665)

RADFORD C., The Maxwell-Dirac Equations, Some Non-Perturbative Results (pages 666-671)

REITY O.K., Asymptotic Expansions of the Potential Curves of the Relativistic Quantum-Mechanical Two-Coulomb-Centre Problem (pages 672-675)

REITY O.K. and LAZUR V.Yu., WKB Method for the Dirac Equation with the Central-Symmetrical Potential and Its Application to the Theory of Two Dimensional Supercritical Atoms (pages 676-682)

ROKHNIZADEH R. and DOEBNER H.D., Geometric Formulation of Berezin Quantization (pages 683-687)

SPICHAK S., On Multi-Parameter Families of Hermitian Exactly Solvable Matrix Schr\"odinger Models (pages 688-690)

SVETLICHNY G., Nonlinear Schr\"odinger Equations for Identical Particles and the Separation Property (pages 691-698)

Related Problems of Mathematical Physics

SHAPOVALOV A. and TRIFONOV A., Semiclassically Concentrates Waves for the Nonlinear Schr\"odinger Equation with External Field (pages 701-711)

BERTI M., Arnold Diffusion: a Functional Analysis Approach (pages 712-719)

BLYUSS K.B., Melnikov Analysis for Multi-Symplectic PDEs (pages 720-724)

CHIRICALOV V.A., Smoothness Properties of Green’s-Samoilenko Operator-Function the Invariant Torus of an Exponentially Dichotomous Bilinear Matrix Differential System (pages 725-729)

KONDAKOVA S., Systems of Linear Differential Equations of Rational Rank with Multiple Root of Characteristic Equation (pages 730-733)

KOROSTIL A.M., On the Spectral Problem for the Finite-Gap Schr\"odinger Operator (pages 734-740)

MATSYUK R.Ya., A Covering Second-Order Lagrangian for the Relativistic Top without Forces (pages 741-745)

NAPOLI A., MESSINA A. and TRETYNYK V., General Even and Odd Coherent States as Solutions of Discrete Cauchy Problems (pages 746-750)

PELYKH V., Knot Manifolds of Double-Covariant Systems of Elliptic Equations and Preferred Orthonormal Three-Frames (pages 751-755)

SHKIL M. and ZAVIZION G., The Asymptotic Solutions of the Systems of Nonlinear Differential Equations (pages 756-759)

TAJIRI M., Asynchronous Development of the Growing-and-Decaying Mode (pages 760-764)

VUS A., Integrable Polynomial Potentials in N-Body Problems on the Line (pages 765-767)

ZHALIJ A., Towards Classification of Separable Pauli Equations (pages 768-773)

ZHEDANOV A. and KOROVNICHENKO A., Leonard Pairs in Classical Mechanics (pages 774-776)

ZNOJIL M., Generalized Rayleigh-Schr\"odinger Perturbation Theory as a Method of Linearization of the so Called Quasi-Exactly Solvable Models (pages 777-781)

NIKITIN A.G., Conclusion (pages 782-783)

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