QUASI-PERIODIC SOLUTIONS OF THE COUPLED NONLINEAR SCHRODINGER-EQUATIONS

We consider travelling periodic and quasi-periodic wave solutions of a set of coupled nonlinear Schrodinger equations. In fibre optics these equations can be used to model single mode fibres under the action of cross-phase modulation, with weak birefringence. The problem is reduc ed to the '1:2:1' integrable case of the two-particle quartic potentia l. A general approach for finding elliptic solutions is given. New sol utions which are associated with two-gap Treibich-Verdier potentials a re found. General quasi-periodic solutions are given in terms of two d imensional theta functions with explicit expressions for frequencies i n terms of theta constants. The reduction of quasi-periodic solutions to elliptic functions is discussed.