ABSTRACT
This chapter considers the extension of the microscopic theory to the case of a condensate structure which varies in space and time. The theory displays clearly the microscopic origin of the macroscopic theory of condensate motion. The chapter considers the problem of arbitrary condensate motion. The condensate motion is influenced by the degree of excitation of the system, so that the two stages of solution are not distinct. What is required is a self-consistent solution, which takes into account the coupling between the condensate and the elementary excitations. The chapter discusses whether the wave functions we have proposed for various simple physical situations are, in fact, consistent with the non-linear condensate equation of motion. It describes a moving condensate, with a uniform density and a slowly varying velocity. The chapter comments briefly on the validity of the factorization approximation.
