  The two-dimensional cubic nonlinear Schr\"{o}dinger equation is used to
describe the propagation of an intense laser beam through a medium with Kerr
nonlinearity. The coupled two-dimensional cubic nonlinear Schr\"{o}dinger
equations are used to describe interaction of electromagnetic waves with
different polarizations in nonlinear optics. In this paper, we solve the above
equations by imposing a quadratic condition on the related argument functions
and using their symmetry transformations. More complete families of exact
solutions of such type are obtained. Many known interesting solutions, such
soliton ones, turn out to be special cases of our solutions.
