Related papers: Discrete nonlinear Schr\"{o}dinger equation in com…
We study a fractional version of the two-dimensional discrete nonlinear Schr\"{o}dinger (DNLS) equation, where the usual discrete Laplacian is replaced by its fractional form that depends on a fractional exponent $s$ that interpolates…
We examine a fractional version of the discrete Nonlinear Schr\"{o}dinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual nearest-neighbor…
We study localization, pinning, and mobility in the fractional discrete nonlinear Schr\"odinger equation (fDNLS) with generalized power-law coupling. A finite-dimensional spatial-dynamics reduction of the nonlocal recurrence yields onsite…
We study the existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the…
We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the…
We show that nonlinear tight-binding lattices of different geometries and dimensionalities, display an universal selftrapping behavior. First, we consider the single nonlinear impurity problem in various tight-binding lattices, and use the…
Local and global existence of localized solutions of a discrete nonlinear Schrodinger (DNLS) equation, with arbitrary on-site nonlinearity, is proved. In particular, it is shown that an initially localized excitation persists localized…
In the present work we explore the potential of models of the discrete nonlinear Schr\"odinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously…
We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue…
We elaborate a fractional discrete nonlinear Schr\"{o}dinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its L\'{e}vy index (LI). This FDNLS equation…
We consider discrete nonlinear Schr\"odinger equations (DNLS) on the lattice $h\mathbb{Z}^d$ whose linear part is determined by the discrete Laplacian which accounts only for nearest neighbor interactions, or by its fractional power. We…
The fractional discrete nonlinear Schr\"odinger equation (fDNLS) is studied on a periodic lattice from the analytic and dynamic perspective by varying the mesh size $h>0$ and the nonlocal L\'evy index $\alpha \in (0,2]$. We show that the…
We consider nonlinear dynamics in a finite parity-time-symmetric chain of the discrete nonlinear Schr{\"o}dinger (dNLS) type. We work in the range of the gain and loss coefficient when the zero equilibrium state is neutrally stable. We…
In the present work we revisit the issue of the self-trapping dynamical transition at a nonlinear impurity embedded in an otherwise linear lattice. For our Schr\"odinger chain example, we present rigorous arguments that establish necessary…
Discrete nonlinear Schr\"oginger equation (DNLS) of the form, $i \frac{dC_n} {dt}$ = $C_{n+1}$ + $C_{n-1}$ - $ \chi_n [|C_{n+1}|^2 + |C_{n-1}|^2 - 2 |C_n|^2] C_n$ is used to study the formation of stationary localized states in one…
We study the statistical mechanics of the one-dimensional discrete nonlinear Schr\"odinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. {\bf 84}, 3740 (2000)] regarding the…
We study the initial-boundary value problem for the derivative nonlinear Schr\"odinger (DNLS) equation. More precisely we study the wellposedness theory and the regularity properties of the DNLS equation on the half line. We prove almost…
The study of nonlinear Schr\"odinger-type equations with nonzero boundary conditions define challenging problems both for the continuous (partial differential equation) or the discrete (lattice) counterparts. They are associated with…
We analyze the nature of a novel type of self-trapping transition called self-localization (SL) of Bose-Einstein condensates in one-dimensional optical lattices in the presence of weak local dissipation. SL has recently been observed in…
Discrete nonlinear Schrodinger equation (DNLS) describes a chain of oscillators with nearest neighbor interactions and a specific nonlinear term. We consider its modification with long-range interaction through a potential proportional to…