Resonant soliton scattering by topological states of a finite array of reflectionless potential wells

Abstract

We investigate bright soliton scattering by periodic reflectionless potential wells. We find sharp transitions in transport coefficients occurring at specific initial soliton speeds. Investigating the band structure of the periodic potential, it turns out that sharp transitions occur at resonance between the energy of the incident soliton and mid-gap topological edge states. Two types of topological states were found: nodal and nodeless states. Stability analysis shows that nodal states are unstable while nodeless are stable against perturbations in equilibrium position.

Keywords: Resonant scattering, Solitons, Topological edge states