Free expansion of fermionic dark solitons in a boson-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic dark solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a harmonic as well as a periodic optical-lattice potential. The dark soliton with a 'notch' in the probability density with a zero at the minimum is simulated numerically as a nonlinear continuation of the first vibrational excitation of the linear mean-field-hydrodynamic equations, as suggested recently for pure bosons. We study the free expansion of these dark solitons as well as the consequent increase in the size of their central notch and discuss the possibility of experimental observation of the notch after free expansion.

Bose-Einstein condensates with inhomogeneous scattering length in one and two dimensions

We report on investigations of the properties of bright solitons in Bose-Einstein condensates in the presence of point-like spatial inhomogeneities, in one and two dimensions. By considering an analytical variational approach and full numerical simulations, we describe such processes due to interactions between the soliton and the inhomogeneity as the trapping, reflection, and transmission of bright matter solitons. We also study the critical number of particles as a function of the magnitude of the impurity.

Three-dimensional solitons in cross-combined linear and nonlinear optical lattices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonautonomous mixed mKdV-sinh-Gordon hierarchy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The higher grading structure of the WKI hierarchy and the two-component short pulse equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A class of mixed integrable models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical and variational solutions of the dipolar Gross-Pitaevskii equation in reduced dimensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Solitary waves on a free surface of a heated Maxwell fluid

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics of quasi-one-dimensional bright and vortex solitons of a dipolar Bose-Einstein condensate with repulsive atomic interaction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Integrable NLS equation with time-dependent nonlinear coefficient and self-similar attractive BEC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Gap solitons in a model of a superfluid fermion gas in optical lattices

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gap solitons in a dipolar Bose-Einstein condensate on a three-dimensional optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Gap solitons in fermion superfluids

We consider a dynamical model of a superfluid Fermi gas in the Bardeen-Cooper-Schrieffer regime trapped in a periodic optical lattice (OL) potential. The model is based on an equation for complex order parameter phi of the superfluid, which is derived from the relevant energy density and includes a self-repulsive term similar to phi(7/3). By means of the variational approximation (VA) and numerical simulations, we find families of stable one- and two-dimensional (I D and 2D) gap solitons (GSs) in this model. Chiefly, they are compact objects trapped in a single cell of the OL. Families of stable even and odd bound states of these GSs are also found in one dimension. A 3D GS family is constructed too, but solely within the framework of the VA. In the linear limit, the VA predicts an almost exact position of the left edge of the first band-gap in the OL-induced spectrum. The full VA provides an accurate description of families of I D and 2D fundamental GSs. We also demonstrate that a I D GS can be safely transported by an OL moving at a moderate velocity. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

Integrablility of a classical N=2 super sinh-Gordon model with jump defects

The Lagrangian formalism for the N = 2 supersymmetric sinh-Gordon model with a jump defect is considered. The modified conserved momentum and energy are constructed in terms of border functions. The supersymmetric Backlund transformation is given and an one-soliton solution is obtained.The Lax formulation based on the affine super Lie algebra sl(2, 2) within the space split by the defect leads to the integrability of the model and henceforth to the existence of an infinite number of constants of motion.

Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)