Long-lived nonlinear oscillatory states in interacting relativistic Bose-Einstein condensates

We study a mean-field model for the dynamics of an interacting Bose-Einstein condensate in two-dimensional pseudorelativistic materials. This model is relatively simple but contains long-lived solutions called oscillons which are absent in simple nonrelativistic condensates. We report on a variety of scenarios including interactions between pairs of oscillons and oscillons propagating across an inhomogeneous material boundary. Hitherto, relativistic oscillons have been studied only in high-energy physics and cosmology, and their relevance has not been highlighted so far in condensed-matter physics.