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 …

Using Lie group theory and canonical transformations, we construct explicit solutions of
nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present …

We report the existence and stability of lattice solitons in parity-time (PT)-symmetric mixed
linear-nonlinear optical lattices in Kerr media. We focus on studying the characteristic effects …

It is shown that using the similarity transformations, a set of three-dimensional pq nonlinear
Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one …

The problem with the construction of the Gross-Pitaevskii (GP) equation and related wave
functions in a medium is associated with the necessity to begin with a description 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 …

Properties of localized states on array of BEC confined to a potential, representing
superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice …

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 …

We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi (BF) mixture
in a double-well potential (DWP). The mixture is described by the Gross-Pitaevskii equation …

We study the existence and stability of solitons forming in PT–symmetric optical lattices with
spatially periodic modulation of the local strength of the nonlinear media. We found that the …