Investigation of Q-tubes stability using the piecewise parabolic potential

Understand

We analyze the classical stability of Q-tubes --- charged extended objects in $(3+1)$-dimensional complex scalar field theory.

• Explicit solutions were found analytically in the piecewise parabolic potential.
• Our choice of potential allows us to construct a powerful method of stability investigation.
• We check that in the case of the zero winding number $n=0$, the previously known stability condition $\partial^2E/\partial Q^2<0$ for Q-balls is fulfilled.