brainwave vs brain wave

brainwave and brain wave both are nouns.

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

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

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

Other synonyms of brainwave include cortical potential.

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