Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics -

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Résumé :
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.

Sommaire:
Hidden and nonlocal symmetries of nonlinear differential equations. Internal symmetries of differential equations. Examples of completely integrable Bateman pairs. Group method analysis of the dispersion of gaseous pollutants in the presence of a temperature inversion. Conformal invariance, Huygens principle and fundamental solutions for scalar second order hyperbolic equations. Potential symmetries and equivalent conservation laws. Some remarks on a class of ordinary differential equations: the Riccati property. Differential-algebraic and differential-geometric approach to the study of involutive symbols. The bihamiltonian approach to integrable systems. Exact solutions of the Boltzmann equation. Einstein equations with 1 parameter spacelike isometry group. Lie point symmetries and dynamical systems. Symmetries of the nonlinear heat equation. Symmetries of time dependent Hamiltonian systems. Quasilinear hyperbolic systems: reduction to autonomous form and wave propagation. Finite difference models entirely inheriting symmetry of original differential equations. Boundary condition invariance. Nonlinear differential equations, Lie symmetries, and the Painlev? test. Non-iterative transformation methods equivalence. Reduction procedures for a class of rate-type materials. Conditional symmetries of the equations of mathematical physics. Pseudopotential symmetries for integrable evolution equations. Isomorphism verification for complex and real Lie algebras by Gr?bner basis technique. sl (2, R), Ermakov systems and the magnetic monopole. Symmetries of differential equations on a lattice. An example: the Toda lattice. Symmetries of particle Lagrangians. The group analysis algorithms. Potential symmetries of Fokker-Planck equations. Continuous symmetries of difference equations. Integrable mechanical systems invariant with respect to the action of the KdV hierarchy. A point symmetry group of a differential equation whichcannot be found using infinitesimal methods. Ermakov structure in 2+1-dimensional systems. Canonical reduction. Symmetries of second-order differential equations and decoupling. Algorithmic methods for Lie pseudogroups. A special class of B?cklund transformations for certain nonlinear partial differential equations. Symmetry groups of balance equations. On equivalence transformations applied to a non-linear wave equation. An efficiency improved program LIEPDE for determining Lie-symmetries of PDEs. Conditional symmetries and the direct reduction of partial differential equations.