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In this paper we study the smoothness properties of solutions to aone-dimensional coupled nonlinear Schr\"{o}dinger system equations thatdescribes some physical phenomena such as propagation of polarized laser beamsin birefringent Kerr medium in nonlinear optics. We show that the equationsdispersive nature leads to a gain in regularity for the solution. Inparticular, if the initial data $(u_{0},\,v_{0})$ possesses certain regularityand 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.

Gain of regularity for a coupled system of generalized nonlinear Schr\"odinger equations