The Proceedings of SNMP'97

are published in two volumes (Volume 1, pages 1-248, and Volume 2, pages 249-500), Editors M.I. Shkil, A.G. Nikitin and V.M. Boyko, Kyiv, Institute of Mathematics, 1997.

ISBN 966-02-0342-X (general)
ISBN 966-02-0343-8  (for Volume 1)
ISBN 966-02-0344-6  (for Volume 2)

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

!!!!! You can download both parts of Proceedings: pdf (6,85 Mb) or djvu (3 Mb)

We present the full list of articles, which are published in Proceedings of Second International Conference "Symmetry in Nonlinear Mathematical Physics. Memorial  Prof. W. FUSHCHYCH Conference" (in pdf format). Please contact us if you have any difficulties with downloading the files (

Volume 1

Titles (pages 1-2)

A. NIKITIN, Preface (pages 3-3)

Contents (pages 4-6)

List of Participants (pages 7-10)

A. NIKITIN, Scientific Heritage of W. Fushchych (pages 11-20)

B.K. HARRISON, Differential Form Symmetry Analysis of Two Equations Cited by Fushchych (pages 21-33)

P. BASARAB-HORWATH and W. FUSHCHYCH, Implicit and Parabolic Ansatzes: Some New  Ansatzes for Old Equations  (pages 34-47)

M.I. SEROV and M.M. SEROVA, The Conditional Symmetry and Connection Between the Equations of Mathematical Physics (pages 48-52)

R. ZHDANOV, On Conditional Symmetries of Multidimensional Nonlinear Equations of Quantum Field Theory (pages 53-61)

L.F. BARANNYK, B. KLOSKOWSKA and V.V. MITYUSHEV, Invariant Solutions of the Multidimensional Boussinesq Equation  (pages 62-69)

M. EULER and  N. EULER, Symmetries for a Class  of Explicitly Space- and Time-Dependent  (1+1)-Dimensional Wave Equations (pages 70-78)

A.K. LOPATIN, Symmetry in Perturbation Problems (pages 79-88)

Z. JIANG, Lie Symmetries and Preliminary Classification of ${u_n^{(k)}(t)=F{}_n(t,u_{n+a}, \ldots, u_{n+b})}$ (pages 89-97)

A. BARANNYK and I. YURYK, On Some Exact Solutions of Nonlinear Wave Equations (pages 98-107)

J. BECKERS, On Specific Symmetries of the KdV Equation and on New Representations of Nonlinear $sl(2)$-algebras
(pages 108-114)

I.V. KULEMIN and A.G. MESHKOV, To the Classification of Integrable Systems in 1+1 Dimensions (pages 115-121)

V. BOYKO, On New Generalizations of the Burgers and Korteweg-de Vries Equations (pages 122-129)

M.L. GANDARIAS, Nonclassical Potential Symmetries of the Burgers Equation (pages 130-137)

R. CHERNIHA, New Ans\"atze and Exact Solutions for Nonlinear Reaction-Diffusion Equations Arising in Mathematical Biology (pages 138-146)

O. ROMAN, Nonlinear Conformally Invariant Wave Equations and Their Exact Solutions (pages 147-154)

L. BERKOVICH, The Generalized  Emden-Fowler Equation (pages 155-163)

L. BERKOVICH and S. POPOV, Group Analysis of the Ordinary Differential Equations of the Order $n>2$ (pages 164-171)

V. TYCHYNIN, Non-local Symmetry of 3-Dimentional Burgers-Type Equation (pages 172-176)

Z. SYMENOH and I. TSYFRA, Equivalence Transformations and Symmetry of the Schr\"odinger Equation with Variable Potential  (pages 177-184)

N. EULER, O. LINDBLOM, M. EULER and L.-E. PERSSON, The Higher Dimensional Bateman Equation and Painlev\'e Analysis of Nonintegrable Wave Equations (pages 185-192)

V. FEDORCHUK, Subgroup Structure of the Poincar\'e Group $P(1,4)$ and Symmetry Reduction of Five-Dimensional Equations of Mathematical Physics (pages 193-199)

I. YEHORCHENKO, Differential Invariants for a Nonlinear Representation of the Poincar\'e Algebra. Invariant Equations
(pages 200-205)

H. LAHNO, Representations of Subalgebras of a Subdirect Sum of the Extended Euclid Algebras and Invariant Equations (pages 206-210)

A. ANDREITSEV, To Separation of Variables  in a (1+2)-Dimensional Fokker-Planck Equation (pages 211-213)

I. REVENKO, On Exact Solutions of the Lorentz-Dirac-Maxwell Equations (pages 214-216)

M. SEROVA and N. ANDREEVA, Evolution Equations Invariant under the Conformal Algebra  (pages 217-221)

H. POPOVYCH, Generalization of Translation Flows of an Ideal Incompressible Fluid: a Modification of the ''Ansatz'' Method (pages 222-226)

V. POPOVYCH, On Lie Reduction of the MHD Equations to Ordinary Differential Equations (pages 227-231)

M. LUTFULLIN, Symmetry Reduction of Nonlinear Equations of Classical Electrodynamics (pages 232-236)

V.V. BUCHYNCHYK, On Symmetries of a Generalized Diffusion Equation (pages 237-241)

I. FEDORCHUK, Reduction and Some Exact Solutions of the Eikonal Equation (pages 241-244)

O. LEIBOV, On Reduction and Some Exact Solutions of the Euler-Lagrange-Born-Infeld Equation (pages 245-248)

Volume 2

Titles (pages 249-250)

Contents (pages 251-253)

W. KLINK, Quantum Mechanics in Noninertial Reference Frames and Representations of  the Euclidean Line Group (pages 254-261)

G. SVETLICHNY, On Relativistic Non-linear Quantum Mechanics (pages 262-269)

P. NATTERMANN, On (Non)Linear Quantum Mechanics (pages 270-278)

Yu.I. SAMOILENKO, A Fiber Bundle Model of the Ice I$_h$ Structure  (pages 279-286)

R. L\'EANDRE, Spinor Fields over Stochastic Loop Spaces (pages 287-296)

M. SHKIL, S. KOVALENKO and  G. ZAVIZION, On a Mixed Problem for a System of Differential Equations of the
Hyperbolic Type with Rotation Points (pages 297-306)

I. TSYFRA, Conformal Invariance of  the Maxwell-Minkowski Equations (pages 307-312)

V. LAHNO, Symmetry Reduction and Exact Solutions of the $SU(2)$ Yang-Mills Equations (pages 313-320)

R. ANDRUSHKIW and A. NIKITIN, Higher Symmetries of the Wave Equation with Scalar and Vector Potentials (pages 321-327)

S.P. ONUFRIYCHUK and O.I. PRYLYPKO, Higher Order Symmetry Operators for the Sch\"odinger Equation (pages 328-330)

A. SERGEYEV, On Parasupersymmetries in a Relativistic Coulomb Problem for the Modified Stueckelberg Equation (pages 331-335)

S. SAITO, Discrete Integrable Systems and the Moyal Symmetry (pages 336-342)

P. HOLOD, A. KISILEVICH and S. KONDRATYUK, An Orbit Structure for Integrable Equations of Homogeneous and Principal Hierarchies (pages 343-352)

A.M. KOROSTIL and I.A. KOROSTIL, Three-Gap Elliptic Solutions of the KdV Equation (pages 353-358)

R. SMIRNOV, On a Construction Leading to Magri-Morosi-Gel'fand-Dorfman's Bi-Hamiltonian Systems (pages 359-365)

A. SVININ, On Some Integrable System of Hyperbolic Type (pages 366-371)

Yu.S. SAMO\u{I}LENKO, L. TUROWSKA and S. POPOVYCH, Representations of a Cubic Deformation of $su(2)$ and Parasupersymmetric Commutation Relations (pages 372-381)

A. GAVRILIK and N. IORGOV, $q$-Deformed Inhomogeneous Algebras ${U_q(iso_n)}$ and Their Representations (pages 384-392)

S. POPOVYCH, Representation of Real Forms of Witten's First Deformation (pages 393-396)

O. BATSEVYCH, Deformed Oscillators with Interaction (pages 397-402)

Yu. BESPALOV, On Duality for a Braided Cross Product (pages 403-408)

V. SIDORETS and V. VLADIMIROV, On the Peculiarities of Stochastic Invariant Solutions of a Hydrodynamic System Accounting for Non-local Effects (pages 409-417)

Y.Z. BOUTROS, M.B. ABD-EL-MALEK, I.A. EL-AWADI and S.M.A. EL-MANSI, Group Method Analysis of the Potential Equation (pages 418-428)

L.F. BARANNYK and P. SULEWSKI, Exact Solutions of the Nonlinear Diffusion Equation $u_0+\nabla \left[u^{-\frac 45}\nabla u\right] =0$ (pages 429-436)

R. POPOVYCH, On Reduction and $Q$-conditional (Nonclassical) Symmetry (pages 437-443)

R. CHERNIHA and M. SEROV, Lie and Non-Lie Symmetries of Nonlinear Diffusion Equations with Convection Term (pages 444-449)

S. SPICHAK and V. STOGNII, Conditional Symmetry and Exact Solutions of the Kramers Equation (pages 450-454)

L.L. BARANNYK, Symmetry Reduction of a Generalized Complex Euler Equation for a Vector Field (pages 455-462)

L.O. TULUPOVA and A.V. GLEBA, Symmetry Properties of a Generalized System of Burgers Equations (pages 463-466)

O. PANCHAK, Symmetry of Burgers-type Equations with an Additional Condition (pages 467-469)

Yu. PODOSHVELEV, The Symmetry of a Generalized Burgers System (pages 470-472)

V. SMALIJ, A Galilei-Invariant Generalization of the Shiff Equations (pages 473-474)

V.M. SIMULIK and I.Yu. KRIVSKY, Fermionic Symmetries of the Maxwell Equations with Gradient-like Sources (pages 475-482)

V. TYCHYNIN, One Geometrical Model for Non-local Transformations (pages 483-487)

V. LEIFURA, On One Problem of Automatic Control with Turning Points (pages 488-491)

V.M. BULAVATSKYI and I.I. YURYK, Nonlinear Boundary-Value Problem for the Heat Mass Transfer Model (pages 492-494)

J. NIEDERLE, Discrete Symmetries and Supersymmetries -- Powerful Tools for Studying Quantum Mechanical Systems (pages 495-498)

B.K. HARRISON, Remarks for Closing Ceremony (pages 499-499)

A. NIKITIN, Conclusion  (pages 500-500)