Stability of coherent-solitonic states for Gross-Pitaevskii equation with parabolic potential

Abstract

We investigate analytically and numerically the linear stability of coherent-solitonic states of the Gross-Pitaevskii equation with parabolic potential. The two lowest-order states are linearly stable. For small enough nonlinearity, either positive or negative, higher states with low intensity develop a limited number of unstable perturbation modes. When the state intensity is raised above a threshold, its stabilization occurs. The full numerical solution of the Gross-Pitaevskii equation confirms that the linear analysis gives an adequate description of solution stability properties for low-order states and moderate propagation lengths.