Ring-like partially nonlocal extreme wave of a (3+1)-dimensional NLS system with partially nonlocal nonlinearity and external potential

This paper aims to study extreme waves localized in (3+1)-dimensional space based on a (3+1)-dimensional nonautonomous partially nonlocal NLS system under the linear and parabolic potentials, which is simplified into a (2+1)-dimensional autonomous equation via a converting formula. Based on solutions of the autonomous NLS system, an approximate solution of ring-like extreme wave is found. Characteristics and evolution of ring-like extreme wave are explored in an exponential system. The influence of the magnitude and exponential parameters of diffraction on ring-like extreme wave is studied. Moreover, the impact of the Hermite polynomial parameter q, the radius parameter R and the thickness parameter w on ring-like extreme wave is also discussed.