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. 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 whichcannot be found using infinitesimal methods.