On a generalized noncommutative three-dimensional three wave resonant equation

A noncommutative version of a generalized three-dimensional three wave resonant (3D3WR) equation is presented. In the commutative case, the generalized noncommutative 3D3WR equation and its Lax pair can be transformed into the 3D3WR equations and its corresponding Lax pair due to a coordinate transformation. The Lax pair for the generalized 3D3WR equation enables us to find Darboux transformations and binary Darboux transformations easily, which are used to construct two families of quasideterminant solutions