Reflectionless potentials and resonant scattering of flat-top and thin-top solitons

TL;DR

This paper identifies a class of potentials enabling reflectionless scattering of flat-top and thin-top solitons in nonlinear Schrödinger equations, revealing sharp resonances and confirming the reflectionless property through simulations.

Contribution

It introduces a new class of reflectionless potentials for flat-top and thin-top solitons in nonlinear Schrödinger equations, derived via perturbative expansion.

Findings

Reflectionless scattering occurs at specific potentials.

Resonances between full transmission and quantum reflection are observed.

Simulations confirm the reflectionless nature of these potentials.

Abstract

We identify a class of potentials for which the scattering of flat-top solitons and thin-top solitons of the nonlinear Schr\"odinger equation with dual nonlinearity can be reflectionless. The scattering is characterized by sharp resonances between regimes of full transmission and full quantum reflection. Perturbative expansion in terms of the magnitude of radiation losses leads to the general form of reflectionless potentials. Simulating the scattering of flat-top solitons and thin-top solitons confirms the reflectionless feature of these potentials.