A system of coupled NLS equations (integrable and non-integrable) is discussed using a Madelung .uid description. The problem is equivalent with a two- component .uid of densities ρ 1 and ρ 2 and velocities υ 1 and υ 2 , which satisfy equations of continuity and equations of motion. Provided that the nonlinear coupling coe.cients are identical, several periodic solutions, expressed through Jacobi elliptic functions, and localized solutions in the form of bright, dark and grey solitons were obtained in di.erent simplifying conditions (motion with constant but equal veloc- ities, i.e. υ 1 = υ 2 = υ , and equal "energies", i.e. E 1 = E 2 = E; motion with stationary profile of the current velocity). For di.erent "energies" (E 1 ≠ E 2 ) a direct method is used, which can be easily extended to more complex situations (di.erent nonlinear coupling coe.cients, i.e. β and γ).
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