Bound-states spectrum of the nonlinear Schrodinger equation with Poschl-Teller and square-potential wells

We obtain the spectrum of bound states for modified Poschl-Teller and square-potential wells in the nonlinear Schrodinger equation. For a fixed norm of bound states, the spectrum for both potentials turns out to consist of a finite number of multinode localized states. Soliton scattering by these two potentials confirmed the existence of the localized states which form as trapped modes. Critical speed for quantum reflection was calculated using the energies of the trapped modes.

Automated summary

The spectrum of bound states for modified Poschl-Teller and square-potential wells in the nonlinear Schrodinger equation is obtained. It is found that for a fixed norm, both potentials have a spectrum consisting of a finite number of multinode localized states. The existence of these localized states, which form as trapped modes, is confirmed through soliton scattering by the two potentials. The critical speed for quantum reflection is calculated using the energies of the trapped modes.