Quasiperiodic Solutions of the Fibre Optics Coupled Nonlinear   Schr{\"o}dinger Equations
  We consider travelling periodical and quasiperiodical waves in single mode fibres, with weak birefringence and under the action of cross-phase modulation. The problem is reduced to the ``1:2:1" integrable case of the two-particle quartic potential. A general approach for finding elliptic solutions is given. New solutions which are associated with two-gap Treibich-Verdier potentials are found. General quasiperiodic solutions are given in terms of two dimensional theta functions with explicit expressions for frequencies in terms of theta constants. The reduction of quasiperiodic solutions to elliptic functions is discussed. 
P L Christiansen, J C Eilbeck, V Z Enolskii and N A Kostov