This article offers a comprehensive survey of results obtained for solitons and complex
nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially …

This review paper presents an overview of the theoretical and experimental progress on the
study of matter-wave dark solitons in atomic Bose–Einstein condensates. Upon introducing …

The aim of this review is to introduce the reader to some of the physical notions and the
mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein …

We predict that one-and two-dimensional self-bound quantum droplets, forming in Bose–
Einstein condensates in the presence of Lee–Huang–Yang (LHY) quantum corrections to …

We study ordinary solitons and gap solitons (GS's) in the framework of the one-dimensional
Gross-Pitaevskii equation (GPE) with a combination of both linear and nonlinear lattice …

We propose a model of a nonlinear double-well potential (NDWP), alias a double-well
pseudopotential, with the objective to study an alternative implementation of the …

We demonstrate that spatially inhomogeneous defocusing nonlinear landscapes with the
nonlinearity coefficient growing toward the periphery as (1+| r|^ α) support one-and two …

We present a unified approach for qualitative and quantitative analysis of stability and
instability dynamics of positive bright solitons in multidimensional focusing nonlinear media …

We put forward new properties of lattice solitons in materials and geometries where both the
linear refractive index and the nonlinearity are spatially modulated. We show that the …

We analyze the existence and stability of two kinds of self-trapped spatially localized gap
modes, gap solitons and truncated nonlinear Bloch waves, in one-and two-dimensional …