Ichans'ka N. Lie and Conditional Symmetry of Some Nonlinear Evolution Equations

This thesis is devoted to investigation of symmetry properties of nonlinear evolution equations and construction of their exact solutions. The Q-conditional symmetry of two-dimensional heat equations is investigated. The inverse group classification problem is solver for nonlinear evolutionary equations and n-order systems of such equations, which are invariant with respect to the conformal algebra. Symmetries of systems of equations of penetration theory, which describe adiabatic motion of non-viscous compressible fluid, are investigated. Completed classification of third order quasi-linear systems of evolutionary equations invariant with respect to the extended Galilei algebra is carried out.