  In this work we employ a recently proposed bifurcation analysis technique,
the deflated continuation algorithm, to compute steady-state solitary waveforms
in a one-component, two dimensional nonlinear Schr\"odinger equation with a
parabolic trap and repulsive interactions. Despite the fact that this system
has been studied extensively, we discover a wide variety of previously unknown
branches of solutions. We analyze the stability of the newly discovered
branches and discuss the bifurcations that relate them to known solutions both
in the near linear (Cartesian, as well as polar) and in the highly nonlinear
regimes. While deflated continuation is not guaranteed to compute the full
bifurcation diagram, this analysis is a potent demonstration that the algorithm
can discover new nonlinear states and provide insights into the energy
landscape of complex high-dimensional Hamiltonian dynamical systems.
