On Elliptic Solutions of a Coupled Nonlinear Schrödinger System
Physica D: Nonlinear Phenomena
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.
Coupled nonlinear Schrödinger equation, Elliptic solutions, Integrable equation
Wright, Otis C. III, "On Elliptic Solutions of a Coupled Nonlinear Schrödinger System" (2013). Science and Mathematics Faculty Publications. 276.