On elliptic solutions of a coupled nonlinear Schrödinger system

•Elliptic solutions of the Manakov system constructed with real quasiperiod.•Effective parametrization for classification of reality conditions.•Loci of the auxiliary variables used in the integration are determined.•Manakov soliton is recovered in the soliton limit.•Small-wave-modulation limit satisfies linearized dispersion of planewaves.

An explicit formula is obtained for single-phase bounded elliptic solutions of the Manakov system of integrable coupled nonlinear Schrödinger equations in terms of the Weierstrass sigma function with a real quasiperiod. The parametrization is effective in the sense that the reality conditions are completely characterized for each of the three possible couplings: focusing–focusing, defocusing–defocusing and focusing–defocusing. The Manakov soliton is recovered in the soliton limit and the small-wave-modulation limit is shown to satisfy the linearized dispersion relation of planewave solutions.