  We consider travelling periodic and quasiperiodic wave solutions of a set of
coupled nonlinear Schr\"odimger equations. In fibre optics these equations can
be used to model single mode fibers with strong birefringence and two-mode
optical fibres. Recently these equations appear as modes, which describe
pulse-pulse interaction in wavelength-division-multiplexed channels of optical
fiber transmission systems. Two phase quasi-periodic solutions for integrable
Manakov system are given in tems of two-dimensional Kleinian functions. The
reduction of quasi-periodic solutions to elliptic functions is dicussed. New
solutions in terms of generalized Hermite polynomilas, which are associated
with two-gap Treibich-Verdier potentials are found.
