  We illustrate the effect of boundary conditions on the evolution of structure
in Fuzzy Dark Matter. Scenarios explored include the evolution of single,
ground-state equilibrium solutions of the Schr\"odinger-Poisson system, the
relaxation of a Gaussian density fluctuation, mergers of two equilibrium
configurations, and the random merger of many solitons. For comparison, each
scenario is evolved twice, with isolation boundary conditions and periodic
boundary conditions, the two commonly used to simulate isolated systems and
structure formation, respectively. Replacing isolation boundary conditions by
periodic boundary conditions changes the domain topology and dynamics of each
scenario, by affecting the outcome of gravitational cooling. With periodic
boundary conditions, the ground-state equilibrium solution and Gaussian
fluctuation each evolve toward the single equilibrium solitonic core of the
isolated case, but surrounded by a tail, unlike the isolated versions. The case
of head-on, binary mergers illustrates additional effects, caused by the pull
suffered by the system due to the infinite network of periodic images along
each direction of the domain. Binary merger with angular momentum is the first
scenario we found in which the tail has a polynomial profile when using a
periodic domain. Finally, the 3D merger of many, randomly-placed solitonic
cores of different mass makes a solitonic core surrounded by a tail with
power-law-like density profile, for periodic boundary conditions, while
producing a core with a much sharper fall-off in the isolated case. This
suggests that the conclusion of earlier work that the ground-state equilibrium
solution is an attractor for the asymptotic state is true even in 3D and for
general circumstances, but only if gravitational cooling is able to carry mass
and energy off to infinity, which isolation boundary conditions allow, but
periodic ones do not.
