Brainwave is a term associated with an idea or inspiration that suddenly comes to someone's mind. There are different synonyms for the word brainwave that include "epiphany," "insight," "revelation," "illumination," and "aha moment." You can use these synonyms interchangeably depending on the context of the sentence or the mood you want to convey. For example, you can use "epiphany" in an academic or spiritual setting while "insight" is more practical and commonly used in business settings. "Revelation" and "illumination" suggest a deeper understanding of a situation, while "aha moment" is more spontaneous and often associated with sudden realization or understanding.