brain wave vs brainwave

brain wave and brainwave both are nouns.

Word	Noun	Adjective	Verb	Adverb
brain wave	Yes	No	No	No
brainwave	Yes	No	No	No

As nouns, brain wave and brainwave are synonyms defined as:

brain wave and brainwave: (neurophysiology) rapid fluctuations of voltage between parts of the cerebral cortex that are detectable with an electroencephalograph

Other synonyms of brain wave include cortical potential.

brain wave (noun)	brainwave (noun)
(neurophysiology) rapid fluctuations of voltage between parts of the cerebral cortex that are detectable with an electroencephalograph	the clear (and often sudden) understanding of a complex situation
	(neurophysiology) rapid fluctuations of voltage between parts of the cerebral cortex that are detectable with an electroencephalograph