Abstract
$Q$-lumps associated with the noncommutative $\mathbb{C}{P}^{N}$ model in $2+1$ dimensions are constructed. These are solitonic configurations which are time dependent and rotate with constant angular frequency. Energy of the $Q$-lumps is $E=2\ensuremath{\pi}k+\ensuremath{\alpha}|Q|$, and we find that in a regime in which the noncommutativity parameter $\ensuremath{\theta}$ is related to the moduli determining the size of the lumps, it can be viewed to depend on $\ensuremath{\theta}$ via the Noether charge $Q$. We present a collective coordinate-type analysis signalling that $\mathbb{C}{P}^{1}$ $Q$-lumps remain stable under small radiative perturbations.
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