Resonant Soliton Scattering by Double Potential Barriers

Solitons are a unique form of nonlinear waves in nonlinear systems. In our study, we investigated the bright soliton scattering by double potential barriers to test whether resonant tunneling, which is known for linear waves, can also occur for nonlinear waves. We used the nonlinear Schrödinger equation with cubic nonlinearity and Pöschl–Teller double potential barriers. We performed numerical simulations of soliton scattering. The simulations revealed a sharp transition in the transport coefficients at a critical incident speed, indicating a resonance phenomenon where the soliton becomes temporarily trapped between the barriers. The resonance occurs when the soliton energy matches the energy of the nodeless bound state between the barriers. For speeds below the critical speed, full reflection occurred, while higher speeds led to complete transmission. These results confirm that resonance can occur in nonlinear systems similar to the case of linear waves. We also found an interesting result we called a trapping window, where the soliton remains confined between the potential barriers for a period of time. This behavior can be utilized or interpreted as a form of soliton storage. This provides an insight for future developments in optical communication and nonlinear quantum devices.