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Persistent bright solitons in sign-indefinite coupled nonlinear Schrodinger equations with a time-dependent harmonic trap

We introduce a model based on a system of coupled nonlinear Schrodinger (NLS) equations with opposite signs infront of the kinetic and gradient terms in the two equations. It also includes time-dependent nonlinearity coefficients and a parabolic expulsive potential. By means of a gauge transformation, we demonstrate that, with a special choice of the time dependence of the trap, the system gives rise to persistent solitons. Exact single and two-soliton analytical solutions and their stability are corroborated by numerical simulations. In particular, the exact solutions exhibit inelastic collisions between solitons.