TODA SYSTEMS ASSOCIATED WITH LIE ALGEBRAS AND W-ALGEBRAS IN SOME PROBLEMS OF MATHEMATICAL PHYSICS

The work is devoted to the investigation of the non-linear systems of differential equations with partial producers with exponential non-linearitites - Toda system associated with Lie algebras - by means of the group analysis and field theory formalism. The symmetry algebras of the Toda system have been calculated, and their conformal invariancy has been proven, the anomal dimensionalities of the Toda fields have been found. The method for construction of the accurate Goursat problem solution for the Toda systems associated with simple finite-dimensional Lie algebras has been proposed, and the solutions for cases of the A*001 and A*002 algebras have been constructed. The asymptotic decomposition in solution of the Gourset problem for sinus-Gordon equation has been constructed, and the inter-geometric interpretation on the free regular solutions of this equation has been proposedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio