Modern Group Analysis: Advanced Analytical And Computational Methods In Mathematical Physics: Proceedings Of The Internati by N.H. IbragimovModern Group Analysis: Advanced Analytical And Computational Methods In Mathematical Physics: Proceedings Of The Internati by N.H. Ibragimov

Modern Group Analysis: Advanced Analytical And Computational Methods In Mathematical Physics…

byN.H. IbragimovEditorM. Torrisi, A. Valenti

Paperback | October 13, 2012

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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; Bäcklund 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.
Title:Modern Group Analysis: Advanced Analytical And Computational Methods In Mathematical Physics…Format:PaperbackDimensions:393 pages, 24 × 16 × 0.01 inPublished:October 13, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401049084

ISBN - 13:9789401049085


Table of Contents

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 Painlevé 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 Gröbner 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 which cannot 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 Bäcklund 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.