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

•We introduce a CNLS eqn. with opposite signs in front of kinetic and gradient terms.•Lax-pair of the CNLS eqn with temporal parabolic expulsive potential is constructed.•Explicit forms of single and two soliton analytical solutions are constructed.•Generated “Persistent” Solitons whose stability also verified numerically.

We introduce a model based on a system of coupled nonlinear Schrödinger (NLS) equations with opposite signs in front of the kinetic and gradient terms in 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.