We introduce PySiUltraLight, a modification of the PyUltraLight code that
includes self-interaction terms to model the dynamical evolution of axion
fields. PyUltraLight simulates ultralight dark matter dynamics. We will use a
boson mass of $10^{-22} \mathrm{eV}/\mathrm{c}^2$ in this paper. We use
PySiUltraLight to produce collapsing solitons, spatially oscillating solitons,
and exploding solitons which prior analytic work shows will occur with
attractive self-interactions. We test the maximum mass criteria described in
arXiv:1604.05904 for a soliton to collapse when attractive self-interactions
are included. Implementing an approximate Gaussian ansatz for the wave function
of the solitons, we calculate the oscillation frequency as a function of
soliton mass and equilibrium radius in the presence of attractive
self-interactions. We verify our code and that when the soliton mass is below
the critical mass ($M_c = \frac{\sqrt{3}}{2}M_{\mathrm{max}}$) described in
arXiv:1604.05904 and the initial radius is within a specific range, solitons
are unstable and explode. We also analyze both binary soliton collisions and a
soliton rotating around a central mass with attractive and repulsive
self-interactions. We find that when attractive self-interactions are included,
the density profiles get distorted after a binary collision. We also find that
a soliton is less susceptible to tidal stripping when attractive
self-interactions are included. We find that the opposite is true for repulsive
self-interactions in that solitons would be more easily tidally stripped.