Nodal compact $Q$-ball/$Q$-shell in the $\mathbb{C}{P}^N$ nonlinear sigma model

Abstract

Nodal, excited compactons in the $\mathbb{C}{P}^N$ models with V-shaped potentials are analyzed. It is shown that the solutions exist as compact $Q$-balls and $Q$-shells. The solutions have a discontinuity in the second derivative associated with the character of the potential, however, their energy and charge densities are both continuous. The excited $Q$-balls and $Q$-shells are analyzed as electrically neutral and electrically charged objects.

22 pages, 12 figures

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