3D partially nonlocal ring-like Kuznetsov-Ma and Akhmediev breathers of NLS model with different diffractions under a linear potential

The Kuznetsov-Ma (KM) and Akhmediev breathers were intensely investigated in the local circumstance, however the 3D partially nonlocal ring-like KM and Akhmediev breathers are hardly studied. This manuscript aims to analyze the partially nonlocal characteristics of ring-like KM and Akhmediev breathers in view of a 3D partially nonlocal nonlinear Schrodinger model with different diffractions under a linear potential. On account of the phi-to-Phi relation, approximate analytical forms of partially nonlocal ring-like KM and Akhmediev breathers are constructed. Ring-like KM breather presents localized rings in the space, and these rings periodically appear in time axis. With the enlargement of Hermite parameter lambda, the ring number adds as lambda + 1 along the z axis. Ring-like Akhmediev breather presents localized structures in time axis, and ring structures recur in the space. With the amplifying Hermite parameter lambda, the layer number of the structure of the circular extension increases as lambda + 1 along the z axis.