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 …

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 …

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 …

This book introduces and explores modern developments in the well established field of
Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and 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 …

In this review we discuss localization of waves by multiple scattering. In the weak case, also
known as coherent backscattering, there is a twofold enhancement of the reflected intensity …

The presence of spatial inhomogeneity in a nonlinear medium results in the breaking of the
translational invariance of the underlying propagation equation. As a result traveling wave …

Motivated by recent proposals of “collisionally inhomogeneous” Bose-Einstein condensates
(BECs), which have a spatially modulated scattering length, we study the existence and …

It has been recently demonstrated that self-defocusing (SDF) media with cubic nonlinearity,
whose local coefficient grows from the center to the periphery fast enough, support stable …

In this paper, we study the exact solitary wave solutions and periodic wave solutions of the S‐
S equation and give the relationships between solutions and the Hamilton energy of their …