Partially nonlocal bright–dark rogue waves and bright–bright rogue wave pairs of a vector nonlinear Schrödinger equation.

The partially nonlocal vector nonlinear Schrödinger equation governs the partially nonlocal nonlinear response of the self-phase and cross-phase modulations in optics and intra- and interspecies atomic nonlocal interactions in BECs. The influence of different diffractions in x- and y-direction on the excitation of partially nonlocal vector rogue waves is hardly studied. This paper aims to study this issue based on a variable-coefficient (3+1)-dimensional vector nonlinear Schrödinger equation with the partially nonlocal nonlinearity for different diffractions by reducing into a constant-coefficient vector nonlinear Schrödinger equation, whose solutions are used to construct analytical solutions of the variable-coefficient vector equation. Exploiting the nonrecursive Darboux method, partially nonlocal vector bright–dark rogue waves and bright–bright rogue wave pairs are revealed. Versatile excitations of these rogue waves are discussed in the sinusoidal and exponential diffraction systems by comparing the maximal value of the accumulated time with the value of the excited location for rogue wave. For the same value of β 1 or β 2 , with the add of the magnitude β 20 or β 10 of the initial diffraction in the y- or x-direction, the amplitude and widths of maximally or early excited figurations of bright–dark rogue waves both increase in the exponential system. These results in this paper deepen our comprehension of ultrashort wave phenomena found in the various fields of physics and engineering including optics, BECs and plasma. [ABSTRACT FROM AUTHOR]