slow ( adverb ) --VS-- slowly ( adverb )?

An Introduction To English Grammar
Some words can have the same form for both the adjectives and the adverbs: easily, fast, hard, late, slow, quick, long, and words in –ly that are formed from nouns denoting time (hourly, daily). The adverbs slow, quick, and deep also have parallel adverb forms in –ly: slowly, quickly, and deeply. These three adverbs formed without –ly suffix are mainly used with imperatives:
Drive slow,
Come quick,
Dig deep into your pocket for donation.

Cambridge Advanced Learners Dictionary
slow (adverb)
Def.:at a slow speed
I can't walk any slower.
slow-moving traffic
a slow-burning candle
mainly US He drives too slow!

Cambridge Advanced Learners Dictionary
slowly (adverb)
Def.: at a slow speed
Could you please speak more slowly?

The American Heritage Dictionary of the English Language
USAGE NOTE Slow may sometimes be used instead of slowly when it comes after the verb: We drove the car slow. In formal writing slowly is generally preferred. Slow is often used in speech and informal writing, especially when brevity and forcefulness are sought: Drive slow! Slow is also the established idiom