Ebook: Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics: Proceedings of the International Workshop Acireale, Catania, Italy, October 27–31, 1992

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: • classical Lie groups applied for constructing invariant solutions and conservation laws; • conditional (partial) symmetries; • Backlund transformations; • approximate symmetries; • group analysis of finite-difference equations; • problems of group classification; • 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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This volume contains a careful selection of papers presented by leading scientists at the workshop on `Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics' held at Catania in Sicily, October 27--31, 1992.
The thirty-nine contributions presented embrace the following topics:
Classical Lie groups applied to the construction of invariant solutions and conservation laws; conditional (partial) symmetries; B?cklund transformations; approximate symmetries; group analysis of finite-difference equations; problems of group classification and software packages in group analysis.
Together this selection of papers provides excellent reviews of many of the exciting developments in this rapidly expanding branch of applied mathematics.
For researchers in mathematical physics and applied mathematics whose work involves group analysis and its applications.

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This volume contains a careful selection of papers presented by leading scientists at the workshop on `Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics' held at Catania in Sicily, October 27--31, 1992.
The thirty-nine contributions presented embrace the following topics:
Classical Lie groups applied to the construction of invariant solutions and conservation laws; conditional (partial) symmetries; B?cklund transformations; approximate symmetries; group analysis of finite-difference equations; problems of group classification and software packages in group analysis.
Together this selection of papers provides excellent reviews of many of the exciting developments in this rapidly expanding branch of applied mathematics.
For researchers in mathematical physics and applied mathematics whose work involves group analysis and its applications.

Content:
Front Matter....Pages i-xi
Hidden and Nonlocal Symmetries of Nonlinear Differential Equations....Pages 1-5
Internal Symmetries of Differential Equations....Pages 7-21
Examples of Completely Integrable Bateman Pairs....Pages 23-33
Group Method Analysis of the Dispersion of Gaseous Pollutants in the Presence of a Temperature Inversion....Pages 35-41
Applications of the Generalized Symmetry Method....Pages 43-53
Conformal Invariance, Huygens Principle and Fundamental Solutions for Scalar Second Order Hyperbolic Equations....Pages 55-69
Potential Symmetries and Equivalent Conservation Laws....Pages 71-84
Some Remarks on A Class of Ordinary Differential Equations: The Riccati Property....Pages 85-92
Differential-Algebraic and Differential-Geometric Approach to the Study of Involutive Symbols....Pages 93-99
The Bihamiltonian Approach to Integrable Systems....Pages 101-110
Conservation Laws in Dissipative Solids....Pages 111-123
Exact Solutions of the Boltzmann Equation....Pages 125-136
Einstein Equations with 1 Parameter Spacelike Isometry Group....Pages 137-145
Lie Point Symmetries and Dynamical Systems....Pages 147-153
Symmetries of the Nonlinear Heat Equation....Pages 155-171
Symmetries of Time Dependent Hamiltonian Systems....Pages 173-179
Quasilinear Hyperbolic Systems: Reduction to Autonomous Form and Wave Propagation....Pages 181-189
Finite Difference Models Entirely Inheriting Symmetry of Original Differential Equations....Pages 191-201
Boundary Condition Invariance....Pages 203-208
Nonlinear Differential Equations, Lie Symmetries, and the Painlev? Test....Pages 209-215
Non-iterative Transformation Methods Equivalence....Pages 217-221
Reduction Procedures for a Class of Rate-Type Materials....Pages 223-229
Conditional Symmetries of the Equations of Mathematical Physics....Pages 231-239
Pseudopotential Symmetries for Integrable Evolution Equations....Pages 241-244
Isomorphism Verification for Complex and Real Lie Algebras by Gr?bner Basis Technique....Pages 245-254
Symmetries of Differential Equations on a Lattice. An Example: The Toda Lattice....Pages 255-264
Symmetries of Particle Lagrangians....Pages 265-272
The Group Analysis Algorithms....Pages 273-276
Potential Symmetries of Fokker-Planck Equations....Pages 277-289
Continuous Symmetries of Difference Equations....Pages 291-298
Integrable Mechanical Systems Invariant with Respect to the Action of the KDV Hierarchy....Pages 299-302
A Point Symmetry Group of a Differential Equation which cannot be Found Using Infinitesimal Methods....Pages 303-309
Ermakov Structure in 2 + 1-Dimensional Systems. Canonical Reduction....Pages 311-316
Symmetries of Second-Order Differential Equations and Decoupling....Pages 317-328
Algorithmic Methods for Lie Pseudogroups....Pages 329-335
A Special Class of B?cklund Transformations for Certain Nonlinear Partial Differential Equations....Pages 337-344
Symmetry Groups of Balance Equations....Pages 345-352
On Equivalence Transformations Applied to a Non-Linear Wave Equation....Pages 353-365
An Efficiency Improved Program Liepde for Determining Lie-Symmetries of PDES....Pages 367-375
Conditional Symmetries and the Direct Reduction of Partial Differential Equations....Pages 377-385
....Pages 387-393