## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

In this paper, we study the stability and the instability of standing
waves for the nonlinear Schrödinger equation with harmonic potential. We prove
the existence of stable or unstable standing waves under certain conditions on the
power of nonlinearity and the frequency of wave.

DCDS

We consider a stationary nonlinear Schröodinger equation with a repulsive
delta-function impurity in one space dimension. This equation admits a unique
positive solution and this solution is even. We prove that it is a minimizer
of the associated energy on the subspace of even functions of $H^1(\R, \C)$,
but not on all $H^1(\R, \C)$, and study its orbital stability.

keywords:
variational methods.
,
Dirac delta
,
standing waves
,
stability
,
nonlinear Schrödinger equation

DCDS-B

The aim of this paper is to perform a theoretical and numerical study
on the dynamics of vortices in Bose-Einstein condensation
in the case where the trapping potential varies randomly in time.
We take a deterministic vortex solution
as an initial condition for the stochastically fluctuated Gross-Pitaevskii equation,
and we observe the influence of the stochastic perturbation on the evolution.
We theoretically prove that up to times of the order of $\epsilon^{-2}$,
the solution having the same symmetry properties as the vortex
decomposes into the sum of a randomly
modulated vortex solution and a small remainder,
and we derive the equations for the modulation parameter.
In addition, we show that the first order of the remainder,
as $\epsilon$ goes to zero, converges to a Gaussian process.
Finally, some numerical simulations on the dynamics of the vortex solution
in the presence of noise are presented.

## Year of publication

## Related Authors

## Related Keywords

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