  Motivated by the work of J.K.~Jang et al., Nat.~Commun.~{\bf 6}, 7370 (2015),
where the authors experimentally tweeze cavity solitons in a passive loop of
optical fiber, we study the amenability to tweezing of cavity solitons as the
properties of a localized tweezer are varied. The system is modeled by the
Lugiato-Lefever equation, a variant of the complex Ginzburg-Landau equation. We
produce an effective, localized, trapping tweezer potential by assuming a
Gaussian phase-modulation of the holding beam. The potential for tweezing is
then assessed as the total (temporal) displacement and speed of the tweezer are
varied, and corresponding phase diagrams are presented. As the relative speed
of the tweezer is increased we find two possible dynamical scenarios:
successful tweezing and release of the cavity soliton. We also deploy a
non-conservative variational approximation (NCVA) based on a Lagrangian
description which reduces the original dissipative partial differential
equation to a set of coupled ordinary differential equations for the cavity
soliton parameters. We illustrate the ability of the NCVA to accurately predict
the separatrix between successful and failed tweezing. This showcases the
versatility of the NCVA to provide a low-dimensional description of the
experimental realization of the temporal tweezing.
