Partially nonlocal ring-like spatiotemporal superimposed second-order breathers under a harmonic potential

Abstract

By means of reduction expression with solutions of constant-coefficient nonlinear Schrödinger system, analytical partially nonlocal ring-like spatiotemporal superimposed second-order Akhmediev and Ma breather solution is derived from the Darboux approach. In xyt or xyz coordinate, the cylindrical multilayer structure of Akhmediev and Ma breathers is embedded in the center, and rings of Akhmediev breather and plane of Ma breather extend out. Moreover, the influence of the radius and thickness parameters is studied. The Hermite parameter has impact on the layer structure of ring-like superimposed second-order breather in the z direction.