  Building on ideas introduced by Eshelby in 1953, and on recent dynamical
extensions of the Peierls model for screw and edge dislocations, an approximate
equation of motion (EoM) to govern non-uniform dislocation motion under
time-varying stress is derived, allowing for time variations of the core width.
Non-local in time, it accounts for radiative visco-inertial effects and
non-radiative drag. It is completely determined by energy functions computed at
constant velocity. Various limits are examined, including that of vanishing
core width. Known results are retrieved as particular cases. Notably, the EoM
reduces to Rosakis's Model I for steady motion [Rosakis, P., 2001. Supersonic
dislocation kinetics from an augmented Peierls model. Phys. Rev. Lett. 86,
95-98]. The frequency-dependent effective response coefficients are obtained
within the linearized theory, and the dynamical self-force is studied for
abrupt or smooth velocity changes accompanied by core variations in the full
theory. A quantitative distinction is made between low- and high-acceleration
regimes, in relation to occurrence of time-logarithmic behavior.
