Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSolitons in one-dimensional nonlinear Schr{o}dinger lattices with a local inhomogeneity
125
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we analyze the existence, stability, dynamical formation and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schr{o}dinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are: a) the destabilization of the on--site mode centered at the defect in the repulsive case; b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type; c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects; and d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection and pure transmission) of interaction of a moving localized mode with the defect.
rate research
Read More
We study coupled unstaggered-staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schr{o}dinger (DNLS) equations with the self-attractive on-site self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction, on 1D and 2D lattice domains. These mixed modes are of a symbiotic type, as each component in isolation may only carry ordinary unstaggered solitons. While most work on DNLS systems addressed symmetric on-site-centered fundamental solitons, these models give rise to a variety of other excited states, which may also be stable. The simplest among them are antisymmetric states in the form of discrete twisted solitons, which have no counterparts in the continuum limit. In the extension to 2D lattice domains, a natural counterpart of the twisted states are vortical solitons. We first introduce a variational approximation (VA) for the solitons, and then correct it numerically to construct exact stationary solutions, which are then used as initial conditions for simulations to check if the stationary states persist under time evolution. Two-component solutions obtained include (i) 1D fundamental-twisted and twisted-twisted soliton pairs, (ii) 2D fundamental-fundamental soliton pairs, and (iii) 2D vortical-vortical soliton pairs. We also highlight a variety of other transient dynamical regimes, such as breathers and amplitude death. The findings apply to modeling binary Bose-Einstein condensates, loaded in a deep lattice potential, with identical or different atomic masses of the two components, and arrays of bimodal optical waveguides.
Asymptotic reductions of a defocusing nonlocal nonlinear Schr{o}dinger model in $(3+1)$-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then its far-field, in the form of a variety of Kadomtsev-Petviashvilli (KP) equations for right- and left-going waves, is found. KP models includ
We derive a straightforward variational method to construct embedded soliton solutions of the third-order nonlinear Schodinger equation and analytically demonstrate that these solitons exist as a continuous family. We argue that a particular embedded soliton when perturbed may always relax to the adjacent one so as to make it fully stable.
Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such quantum matter arises in a number of different theories, including the Peccei-Quinn axion and UltraLight (ULDM) or Fuzzy (FDM) dark matter scenarios. We consider the dynamical evolution of perturbations to the spherically symmetric soliton, the ground state solution to the Schr{o}dinger-Poisson system common to all these scenarios. We construct the eigenstates of the Schr{o}dinger equation, holding the gravitational potential fixed to its ground state value. We see that the eigenstates qualitatively capture the properties seen in full ULDM simulations, including the soliton breathing mode, the random walk of the soliton center, and quadrupolar distortions of the soliton. We then show that the time-evolution of the gravitational potential and its impact on the perturbations can be well described within the framework of time-dependent perturbation theory. Applying our formalism to a synthetic ULDM halo reveals considerable mixing of eigenstates, even though the overall density profile is relatively stable. Our results provide a new analytic approach to understanding the evolution of these systems as well as possibilities for faster approximate simulations.
We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schr{o}dinger equation with the cubic or cubic-quintic (CQ) nonlinearity and a parity-time (PT)-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of the CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually-conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation, solely in the case of the fractional diffraction. While GSs are not true solutions, direct simulations confirm that their shapes and results of their stability analysis provide a blueprint for the evolution of genuine localized modes in the system.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
