Glieba A. Symmetry properties and exact solutions of nonlinear galiley-invariant equations

Nonlinear galiley-invariant equations. Investigation of symmetry properties and construction of exact solutions. The modern methods of group analysis, Lie's and conditional symmetry, the general theory of differential equations, mathematical physics. The classification of a number of galiley-invariant equations was conducted with respect different representations of Galilean's algebras. The symmetry properties were investigated. Lie's and conditional symmetries were used for building invariants of Galilean's algebra. These invariants were used for building anzatses and reduction equations to ordinary or partial differential equations with a lesser number of unknown values. Exact solutions of investigate equations are built and formulae of generating solutions are received. The results are new and can be used in applied problem of mathematical and theoretical physics, hydrodynamics, quantum mechanics, in the theory of diffusion processes and ets.