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

TL;DR

This paper investigates nodal, excited compact solutions called $Q$-balls and $Q$-shells in the $ ext{CP}^N$ nonlinear sigma model with V-shaped potentials, highlighting their continuous energy and charge densities despite derivative discontinuities.

Contribution

It demonstrates the existence of nodal $Q$-balls and $Q$-shells with discontinuous second derivatives in the $ ext{CP}^N$ model, expanding understanding of compacton solutions.

Findings

Solutions are compact $Q$-balls and $Q$-shells with continuous energy and charge densities.

Discontinuity occurs in the second derivative due to the V-shaped potential.

Both electrically neutral and charged solutions are analyzed.

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.