On a periodic solution of the focusing nonlinear Schr\"odinger equation
  A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is investigated. An existence of a real smooth finite-gap solution of NLS equation with complex initial phase is proven. Degenerations of the constructed solution to one-phase traveling wave solution and solutions in the form of the plane waves are carried. 
A. O. Smirnov, E. G. Semenova, V. Zinger, and N. Zinger
math-ph math.MP nlin.PS nlin.SI