Integrability of multiple three-wave interactions

Numerical evidence is presented which indicates that the N-degree-of-freedom Hamiltonian that describes a set of pairs of sinusoidal waves interacting with a single, "test" wave is completely integrable. Computations of the Poincar\'e surface of section and Greene's residues provide the evidence for two background wave pairs. Linear separation of neighboring orbits for up to four wave pairs also suggests integrability for more degrees of freedom.