Symmetry analysis and exact solutions for nonlinear equations in mathematical physics

The book provides an overview of the current status of theoretical-algebraic methods in relation to linear and nonlinear multidimensional equations in mathematical and theoretical physics that are invariant with respect to the Poincare and Galilean groups and the wider Lie groups. Particular attention is given to the construction, in explicit form, of wide classes of accurate solutions to specific nonlinear partial differential equations, such as nonlinear wave equations for scalar, spinor, and vector fields, Young-Mills equations, and nonlinear quantum electrodynamic equations. A group-theory approach is used to analyze the classical three-body problem.