Resilience of constituent solitons in multisoliton scattering off barriers

Abstract

We introduce "superheated integrability," which produces characteristic staircase transmission plots for barrier collisions of breathers of the nonlinear Schr\"odinger equation. The effect makes tangible the inverse scattering transform, which treats the velocities and norms of the constituent solitons as the real and imaginary parts of the eigenvalues of the Lax operator. If all the norms are much greater than the velocities, an integrability-breaking potential may nonperturbatively change the velocities while having no measurable effect on the norms. This could be used to improve atomic interferometers.