Abstract
We study the response of a $Q$-ball soliton (with an unbroken global Abelian internal symmetry) under an arbitrary perturbation (not necessarily Lagrangian). A method based on dynamical symmetry groups and singular perturbation theory is presented and the dynamics of the collective coordinates that characterize the soliton derived. The method presented here can also be applied to study interacting $Q$ balls perturbed, topological solitons, nontopological solitons with an additional broken discrete symmetry, and nontopological solitons with a non-Abelian internal symmetry group such as, for example, the $Q$ lumps of the nonlinear \ensuremath{\sigma} model with SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) global symmetry.
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