Nonlinear tunneling through a strong rectangular barrier

Nonlinear tunneling is investigated by analytically solving the one-dimensional Gross–Pitaevskii equation (GPE) with a strong rectangular potential barrier. With the help of analytical solutions of the GPE, which can be reduced to the solution of the linear case, we find that only the supersonic solution in the downstream has a linear counterpart. A critical nonlinearity is explored as an up limit, above which no nonlinear tunneling solution exists. Furthermore, the density solution of the critical nonlinearity as a function of the position has a step-like structure.