Identify the complete spectrum of excited solution branches

Identify the additional stable or unstable excitation branches of the gravitating chiral-quark soliton model arising from different balances between valence and Dirac-sea contributions, and determine the full structure of its solution spectrum.

Background

The numerical study primarily obtains ground-state solutions and observes some excited states near the ground state. The authors suggest that further unstable branches may arise from other balances between valence and Dirac-sea contributions.

Those branches were not found by the numerical scheme used in the paper. A more efficient computational method is required to determine whether such branches exist and to characterize the complete excitation spectrum.