  In this work, we introduce a dispersive N(=2n)-wave interaction problem
involving n velocities in two spatial dimensions and one temporal dimension.
Exact solutions of the problem are exhibited. This is a generalization of the
N-wave interaction problem and matrix Davey-Stewartson equation with 2+1
dimensions that examines the Benney-type model of interactions between short
and long waves. Accordingly, associated with the solutions of two dimensional
analog of the Manakov system, a Gelfand-Levitan-Marchenko (GLM)-type, or
so-called inversion-like, equation is constructed. It is shown that the
presence of the degenerate kernel reads exact soliton-like solutions of the
dispersive N-wave interaction problem.We also mention the unique solution of
the Cauchy problem on an arbitrary time interval for small initial data.
