  A generic theory of a single real scalar field is considered, and a simple
method is presented for obtaining a class of solutions to the equation of
motion. These solutions are obtained from a simpler equation of motion that is
generated by replacing a set of the original coordinates by a set of
generalized coordinates, which are harmonic functions in the spacetime. These
ansatz solutions solve the original equation of motion on manifolds that are
defined by simple constraints. These manifolds, and their dynamics, are
independent of the form of the scalar potential. Some scalar field solutions,
and manifolds upon which they exist, are presented for Klein-Gordon and quartic
potentials as examples. Solutions existing on leaves of a foliated space may
allow inferences of the characteristics expected of exact bulk solutions.
