384 research outputs found
Recommended from our members
Parametric Quantum Resonances for Bose–Einstein Condensates
We generalize recent work on parametric resonances for nonlinear Schrödinger (NLS) type equations to the case of three dimensional Bose–Einstein condensates at zero temperatures. We show the possibility of such resonances in the three-dimensional case, using a moment method and numerical simulations
Recommended from our members
Discrete solitons and vortices on anisotropic lattices
We consider the effects of anisotropy on solitons of various types in two-dimensional nonlinear lattices, using the discrete nonlinear Schrödinger equation as a paradigm model. For fundamental solitons, we develop a variational approximation that predicts that broad quasicontinuum solitons are unstable, while their strongly anisotropic counterparts are stable. By means of numerical methods, it is found that, in the general case, the fundamental solitons and simplest on-site-centered vortex solitons (“vortex crosses”) feature enhanced or reduced stability areas, depending on the strength of the anisotropy. More surprising is the effect of anisotropy on the so-called “super-symmetric” intersite-centered vortices (“vortex squares”), with the topological charge S equal to the square’s size M: we predict in an analytical form by means of the Lyapunov-Schmidt theory, and confirm by numerical results, that arbitrarily weak anisotropy results in dramatic changes in the stability and dynamics in comparison with the degenerate, in this case, isotropic, limit
Recommended from our members
On some classes of mKdV periodic solutions
We obtain exact periodic solutions of the positive and negative modified Kortweg–de Vries (mKdV) equations. We examine the dynamical stability of these solitary wave lattices through direct numerical simulations. While the positive mKdV breather lattice solutions are found to be unstable, the two-soliton lattice solution of the same equation is found to be stable. Similarly, a negative mKdV lattice solution is found to be stable. We also touch upon the implications of these results for the KdV equation
Stability of discrete dark solitons in nonlinear Schrodinger lattices
We obtain new results on the stability of discrete dark solitons bifurcating
from the anti-continuum limit of the discrete nonlinear Schrodinger equation,
following the analysis of our previous paper [Physica D 212, 1-19 (2005)]. We
derive a criterion for stability or instability of dark solitons from the
limiting configuration of the discrete dark soliton and confirm this criterion
numerically. We also develop detailed calculations of the relevant eigenvalues
for a number of prototypical configurations and obtain very good agreement of
asymptotic predictions with the numerical data.Comment: 11 pages, 5 figure
Recommended from our members
Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein–Gordon equations
We show decay estimates for the propagator of the discrete Schrödinger and Klein–Gordon equations in the form {{\| {U(t)f} \|}_{{l^\infty}}} \leq C (1+|t|)^{-d/3}{{\| {f} \|}_{{l^1}}} . This implies a corresponding (restricted) set of Strichartz estimates. Applications of the latter include the existence of excitation thresholds for certain regimes of the parameters and the decay of small initial data for relevant lp norms. The analytical decay estimates are corroborated with numerical results
Recommended from our members
An exploding glass?
We propose a connection between self-similar, focusing dynamics in nonlinear partial differential equations (PDEs) and macroscopic dynamic features of the glass transition. In particular, we explore the divergence of the appropriate relaxation times in the case of hard spheres as the limit of random close packing is approached. We illustrate the analogy in the critical case, and suggest a “normal form” that can capture the onset of dynamic self-similarity in both phenomena
Modulational Instability in Bose-Einstein Condensates under Feshbach Resonance Management
We investigate the modulational instability of nonlinear Schr{\"o}dinger
equations with periodic variation of their coefficients. In particular, we
focus on the case of the recently proposed, experimentally realizable protocol
of Feshbach Resonance Management for Bose-Einstein condensates. We derive the
corresponding linear stability equation analytically and we show that it can be
reduced to a Kronig-Penney model, which allows the determination of the windows
of instability. The results are tested numerically in the absence, as well as
in the presence of the magnetic trapping potential
Recommended from our members
Averaging for Solitons with Nonlinearity Management
We develop an averaging method for solitons of the nonlinear Schrödinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations
- …