Exact localized nonlinear vector matter waves in the form of soliton-soliton and vortex-vortex pairs in two-component Bose-Einstein condensates with spatially modulated nonlinearity coefficients and harmonic trapping potentials are reported. It is shown that there exists an infinite number of exact vector pairs sharing the same chemical potential with soliton-soliton ones for odd integer n while vortex-vortex ones for even integer n. The stability of the vector pairs found is investigated by means of direct numerical simulations and a linear stability analysis; the results show that the stable vortex-vortex pairs (±l,±l) with large topological charges can be supported by the spatially modulated interaction when the harmonic trapping potential is presented in this system. © 2012 Elsevier B.V.
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