We consider several effects of the matter wave dynamics which can be observed in Bose–
Einstein condensates embedded into optical lattices. For low-density condensates, we …

We present a progress overview focused on the recent theoretical and experimental
advances in the area of soliton manipulation in optical lattices. Optical lattices offer the …

Using the variational approximation and direct simulations in real and imaginary time, we
find stable two-dimensional (2D) and 3D solitons in the self-attractive Gross-Pitaevskii …

We discuss localized ground states of Bose-Einstein condensates (BEC's) in optical lattices
with attractive and repulsive three-body interactions in the framework of a quintic nonlinear …

We investigate the existence and stability of three-dimensional spatiotemporal solitons in
self-focusing cubic Kerr-type optical media with an imprinted two-dimensional harmonic …

We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-
dimensional Pöschl-Teller potential which contains an asymmetry term. The eigenfunctions …

We predict the existence of spatially localized nontrivial topological states of a Bose-Einstein
condensate with repulsive atomic interactions confined by an optical lattice. These nonlinear …

It has recently been discovered that stabilization of two-dimensional (2D) solitons against
the critical collapse in media with cubic nonlinearity by means of nonlinear lattices (NLs) is a …

We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates
(BECs) subject to strong confinement along the axial direction. Starting from the three …

We show that two-dimensional photonic Kerr nonlinear lattices can support stable soliton
complexes composed of several solitons packed together with appropriately engineered …