Restricted multiple three-wave interactions: Integrable cases of this system and other related systems

Abstract
Restricted multiple three-wave interactions, in which a set of wave triads interact through one shared wave, are discussed. It is shown that this system is integrable when all triads have equal coupling coefficients regardless of the frequency mismatches. This system is then used as a starting point from which to determine integrable cases of a more general class of three-wave interactions.