Bloch oscillations of multidimensional dark soliton wave packets and light bullets

The robust propagation of dark solitonic waves featuring Bloch oscillations (BOs) in media with a Kerr nonlinearity is demonstrated. The models considered have a discrete refractive index gradient in one dimension and are continuous in the orthogonal direction or directions. Such systems can be realized in photonic settings, where temporal dispersion of a normal type is able to support dark solitons. The demonstrated effects may also appear in the dynamics of Bose-Einstein condensates (BECs), where dark solitons appear due to the joint action of diffraction and a self-defocusing nonlinearity. Furthermore, our analysis shows that a periodic variation of the refractive index gradient in the propagation direction allows us to realize the spatial analog of dynamical localization. In addition, we demonstrate that dark solitons serve as excellent supporters for light bullets of a peculiar dark-bright type that can also feature robust BOs.