Nonlinear tunneling of partially nonlocal dark-dark annular sneaker waves under a parabolic potential

Annular rogue waves have been reported, but little is known about how to excite and control them, particularly their tunneling effect. From the projecting relation between the vector partially nonlocal nonlinear Schrödinger equation possessing different transverse-directional diffractions and the parabolic potential and vector constant-coefficient nonlinear Schrödinger equation, via the Darboux method, partially nonlocal dark-dark annular sneaker wave approximate solutions are found. Two aspects of the study are carried out: (i) four excitations of partially nonlocal dark-dark annular sneaker waves including complete, delayed, valley-maintained and prohibitive excitations and (ii) nonlinear tunneling of partially nonlocal dark-dark annular sneaker waves are studied. The influence of two parameters $R$ and $l$ on dark-dark annular sneaker waves is also analyzed. The partially nonlocal characteristics of dark-dark annular sneaker waves passing through the nonlinear well implies that the layer of annular sneaker wave structures increases in $xyz$-coordinate when the value of the Hermite parameter adds. These findings will further our understanding of the partially nonlocal nonlinear wave in the disciplines of cold atom and optical communication.