by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works 55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The...

This volume presents an account of the current state of algebraic-theoretic methods as applied to linear and nonlinear multidimensional equations of mathematical and theoretical physics. Equations are considered that are invariant under Euclid, Galilei, Schrodinger, Poincare, conformal, and some other Lie groups, with special emphasis being given to the construction of wide classes of exact solutions of concrete nonlinear partial differential equations, such as d'Alembert, Liouville, Monge-Ampere, Hamilton-Jacobi, eikonal, Schrodinger, Navier-Stokes, gas dynamics, Dirac, Maxwell-Dirac,...

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Guik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It...