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

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.- Applications of the generalized symmetry method.- 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.- Conservation laws in dissipative solids.- 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.- Thegroup 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.