GROUP-THEORY AND SOLUTIONS OF CLASSICAL FIELD-THEORIES WITH POLYNOMIAL NONLINEARITIES

In this paper we investigate a number of analytical solutions to the p olynomial class of nonlinear Klein-Gordon equations in multidimensiona l spacetime. This is done in the context of classical phi4 and phi6 fi eld theory, the former with and without the inclusion of an external f orce field conjugate to phi. Both massive (m not-equal 0) and massless (m = 0) cases are considered, as well as tachyonic solutions allowed (v > c). We first present a complete set of translationally invariant solutions for the phi4 model and demonstrate the role of external forc e fields in altering the form of these solutions. Next, spherically sy mmetric solutions are discussed in both phi4 and phi4 cases since they provide the most realistic models of elementary particles.