  The Davey-Stewartson 1(DS1) system[9] is an integrable model in two
dimensions. A quantum DS1 system with 2 colour-components in two dimensions has
been formulated. This two-dimensional problem has been reduced to two
one-dimensional many-body problems with 2 colour-components. The solutions of
the two-dimensional problem under consideration has been constructed from the
resulting problems in one dimensions. For latters with the $\delta $-function
interactions and being solved by the Bethe ansatz, we introduce symmetrical and
antisymmetrical Young operators of the permutation group and obtain the exact
solutions for the quantum DS1 system. The application of the solusions is
discussed.
