Quasi-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Q</mml:mi></mml:math>-balls in massless scalar fields

We study long-term evolution of radiating quasi-Q-balls in 1+1 dimensional models without mass threshold. Two different models are considered, the model with a rational modification of the usual Q-ball sextic potential and the model of a Q-ball in a box with outgoing boundary conditions. We find that the outgoing boundary conditions modify the angular frequency of quasi-Q-balls which becomes complex-valued. The quasi-Q-balls decay initially very similarly but, in the last stage, quasi-Q-balls in a box become linear resonances, whereas in the rationally modified model, they decay according to some power law.