Abstract
Dark solitons collision in an ultracold neutral plasma in the framework of the phenomenological generalized hydrodynamic model is reported. The derivative expansion method is used to derive a nonlinear Schrödinger equation for describing the low frequency modulation. The critical wavenumber kc, which indicates where the modulational instability sets in, is determined precisely. Also, the modulationally stable and unstable regions are obtained for a wide range of the wavenumber k and the ions effective temperature ratio . In the stable regions, the collisions between two-dark solitons are investigated using the extended Poincaré-Lighthill-Kuo method and their corresponding phase shifts are derived. The dependence of both and k on the phase shift is examined.