High-speed soliton ejection generated from the scattering of bright solitons by modulated reflectionless potential wells

Bound-states spectrum of the nonlinear Schrödinger equation with Pöschl-Teller and square-potential wells

We obtain the spectrum of bound states for modified Pöschl-Teller and square-potential wells in the nonlinear Schrödinger 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.

Quantum reflection of dark solitons scattered by reflectionless potential barrier and position-dependent dispersion

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.