Related papers: Stationary Localized States Due to a Nonlinear Dim…
The Discrete Nonlinear Schr$\ddot{o}$dinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The…
The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a…
We investigate the effect of a nondegenerate quadratic nonlinear dimeric impurity on the formation of stationary localized states in one dimensional systems. We also consider the formation of stationary localized states in a fully nonlinear…
Formation of stationary localized states in one-dimensional chain due to a linear impurity and a modified nonlinear impurity is studied. Furthermore, a one-dimensional chain with linear and modified nonlinear site energies at the alternate…
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…
Formation of stationary localized states in one-dimensional chain as well as in a Cayley tree due to a linear impurity and a nonlinear impurity is studied. Furthermore, a one-dimensional chain with linear and nonlinear site energies at the…
We study the formation of stationary localized states using the discrete nonlinear Schr\"{o}dinger equation in a Cayley tree with connectivity $K$. Two cases, namely, a dimeric power law nonlinear impurity and a fully nonlinear system are…
A new 1-D discrete nonlinear Schr\"{o}dinger (NLS) Hamiltonian is introduced which includes the integrable Ablowitz-Ladik system as a limit. The symmetry properties of the system are studied. The relationship between intrinsic localized…
We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schr{\"o}dinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity and…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
We examine the formation of localized states on a generalized nonlinear impurity located at, or near the surface of a semi-infinite 2D square lattice. Using the formalism of lattice Green functions, we obtain in closed form the number of…
We introduce a one-dimensional model based on the nonlinear Schrodinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters…
We study the unitary relaxation dynamics of disordered spin chains following a sudden quench of the Hamiltonian. We give analytical arguments, corroborated by specific numerical examples, to show that the existence of a stationary state…
The semi-infinite XY spin chain with an impurity at the boundary has been chosen as a prototype of interacting many-body systems to test for non-ergodic behavior. The model is exactly solvable in analytic way in the thermodynamic limit,…
We consider the eigenvalue problem for one-dimensional linear Schr\"odinger lattices (tight-binding) with an embedded few-sites linear or nonlinear, Hamiltonian or non-conservative defect (an oligomer). Such a problem arises when…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
IN-DNLS, considered here is a countable infinite set of coupled one dimensional nonlinear ordinary differential difference equations with a tunable nonlinearity parameter, $\nu$. This equation is continuous in time and discrete in space…
Discrete dissipative coupled systems exhibit complex behavior such as chaos, spatiotemporal intermittence, chimera among others. We construct and investigate chimera states, in the form of confined stationary and dynamical states in a chain…
Strong evidence is presented for the localization of low energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite…
This paper focuses on the analysis of an optimal control problem governed by a nonsmooth quasilinear partial differential equation that models a stationary incompressible shear-thickening fluid. We start by studying the directional…