Present participle of doven; behaving like a dove or cooing softly.
From 'doven' plus the present participle suffix '-ing,' which creates the 'ing' form of verbs used in progressive tenses and as gerunds.
Using '-ing' forms of archaic verbs lets writers be super poetic—'she was dovening her love' sounds way more lyrical than 'she was cooing softly,' which is probably why poets kept using these old forms.
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