  In this paper we study the smoothness properties of solutions to a
one-dimensional coupled nonlinear Schr\"{o}dinger system equations that
describes some physical phenomena such as propagation of polarized laser beams
in birefringent Kerr medium in nonlinear optics. We show that the equations
dispersive nature leads to a gain in regularity for the solution. In
particular, if the initial data $(u_{0},\,v_{0})$ possesses certain regularity
and sufficient decay as $|x|\rightarrow\infty,$ then the solution
$(u(t),\,v(t))$ will be smoother than $(u_{0},\,v_{0})$ for $0 < t \leq T$
where $T$ is the existence time of the solution.
