Stability of Q-balls and catastrophe

We propose a practical method for analyzing stability of Q-balls for the whole parameter space, which includes the intermediate region between the thin-wall limit and thick-wall limit as well as Q-bubbles (Q-balls in false vacuum), using catastrophe theory. We apply our method to the two concrete models, V(3) = m(2)phi(2) /2-mu phi(3) + lambda phi(4) and V(4) = m(2)phi(2)/2-lambda phi(4) + phi(6)/M(2). We find that V(3) and V(4) Models fall into fold catastrophe and cusp catastrophe, respectively, and their stability structures are quite different from each other.