Modern Group Analysis

Advanced Analytical and Computational Methods in Mathematical Physics : Proceedings of the International Workshop Acireale, Catania, Italy, October 27-31, 1992

By: N.H. Ibragimov (Editor), M. Torrisi (Editor), A. Valenti (Editor)

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Hardcover | 30 September 1993

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408 Pages

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On the occasion of the 150th anniversary of Sophus Lie, an International Work shop "Modern Group Analysis: advanced analytical and computational methods in mathematical physics" has been organized in Acireale (Catania, Sicily, October 27 31, 1992). The Workshop was aimed to enlighten the present state ofthis rapidly expanding branch of applied mathematics. Main topics of the Conference were: â¢ classical Lie groups applied for constructing invariant solutions and conservation laws; â¢ conditional (partial) symmetries; â¢ Backlund transformations; â¢ approximate symmetries; â¢ group analysis of finite-difference equations; â¢ problems of group classification; â¢ software packages in group analysis. The success of the Workshop was due to the participation of many experts in Group Analysis from different countries. This book consists of selected papers presented at the Workshop. We would like to thank the Scientific Committee for the generous support of recommending invited lectures and selecting the papers for this volume, as well as the members of the Organizing Committee for their help. The Workshop was made possible by the financial support of several sponsors that are listed below. It is also a pleasure to thank our colleague Enrico Gregorio for his invaluable help of this volume.

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Non-Fiction Science Physics Mathematical Physics Mathematics Calculus & Mathematical Analysis Numerical Analysis Groups & Group Theory Differential Calculus & Equations Algebra

Hidden and nonlocal symmetries of nonlinear differential equations	p. 1
Internal symmetries of differential equations	p. 7
Examples of completely integrable Bateman pairs	p. 23
Group method analysis of the dispersion of gaseous pollutants in the presence of a temperature inversion	p. 35
Applications of the generalized symmetry method	p. 43
Conformal invariance, Huygens principle and fundamental solutions for scalar second order hyperbolic equations	p. 55
Potential symmetries and equivalent conservation laws	p. 71
Some remarks on a class of ordinary differential equations: the Riccati property	p. 85
Differential-algebraic and differential-geometric approach to the study of involutive symbols	p. 93
The bihamiltonian approach to integrable systems	p. 101
Conservation laws in dissipative solids	p. 111
Exact solutions of the Boltzmann equation	p. 125
Einstein equations with 1 parameter spacelike isometry group	p. 137
Lie Point symmetries and dynamical systems	p. 147
Symmetries of the nonlinear heat equation	p. 155
Symmetries of time dependent Hamiltonian systems	p. 173
Quasilinear hyperbolic systems: reduction to autonomous form and wave propagation	p. 181
Finite difference models entirely inheriting symmetry of original differential equations	p. 191
Boundary condition invariance	p. 203
Nonlinear differential equations, Lie symmetries, and the Painleve test	p. 209
Non-iterative transformation methods equivalence	p. 217
Reduction procedures for a class of rate-type materials	p. 223
Conditional symmetries of the equations of Mathematical Physics	p. 231
Pseudopotential symmetries for integrable evolution equations	p. 241
Isomorphism verification for complex and real Lie algebras by Grobner basis technique	p. 245
sl(2, R), Ermakov systems and the magnetic monopole	p. 255
Symmetries of differential equations on a lattice. An example: the Toda Lattice	p. 265
Symmetries of particle Lagrangians	p. 273
The group analysis algorithms	p. 277
Potential symmetries of Fokker-Planck equations	p. 291
Continuous symmetries of difference equations	p. 299
Integrable mechanical systems invariant with respect to the action of the KdV hierarchy	p. 303
A point symmetry group of a differential equation which cannot be found using infinitesimal methods	p. 311
Ermakov structure in 2 + 1-dimensional systems. Canonical reduction	p. 317
Symmetries of second-order differential equations and decoupling	p. 329
Algorithmic methods for Lie pseudogroups	p. 337
A special class of Backlund transformations for certain nonlinear partial differential equations	p. 345
Symmetry groups of balance equations	p. 353
On equivalence transformations applied to a non-linear wave equation	p. 367
An efficiency improved program LIEPDE for determining Lie-symmetries of PDEs	p. 377
Conditional symmetries and the direct reduction of partial differential equations	p. 387
Table of Contents provided by Blackwell. All Rights Reserved.

Modern Group Analysis

Advanced Analytical and Computational Methods in Mathematical Physics : Proceedings of the International Workshop Acireale, Catania, Italy, October 27-31, 1992

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