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.