This article is from the Star Trek Tech FAQ, by Joshua Bell inexorabletash@hotmail.com with numerous contributions by others.
The Tech Manual states that the subspace field generators coupled to
the Impulse drive can be used to maintain a decaying subspace field
for brief periods of time. The decay is inevitable, but it can be
drawn out, to allow the saucer section to get out of danger.
By field-saturating the nacelles (according to "Force of Nature"
[TNG]), after a 6 second burst of maximum warp the Enterprise can
"coast" at warp for 2 minutes 8 seconds before dropping out of warp.
This is a form of "warp without warp drive", although the effect does
not last very long.
This is similar to how photon torpedoes can be used at warp speeds.
They have small "warp sustainer" engines that allow them to cruise at
their launch velocity (if launched while in warp) for brief periods.
 
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