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

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

Mean-field equations for cigar- and disc-shaped Bose and Fermi superfluids

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

Nonlinear Gravitational Waves: Their Form and Effects

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)

GALACTIC NONLINEAR DYNAMIC MODEL

We develop a model for spiral galaxies based on a nonlinear realization of the Newtonian dynamics starting from the momentum and mass conservations in the phase space. The radial solution exhibits a rotation curve in qualitative accordance with the observational data.

On the solutions of the position-dependent effective mass Schrodinger equation of a nonlinear oscillator related with the isotonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Superfluid Bose-Fermi mixture from weak coupling to unitarity

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

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Nonlinear Schrodinger equation for a superfluid Fermi gas in the BCS-BEC crossover

We introduce a quasianalytic nonlinear Schrodinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where k(F)parallel to a parallel to << 1 with a the s-wave scattering length and k(F) the Fermi momentum, through the unitarity limit k(F)a ->+/-infinity to the Bose-Einstein condensation (BEC) regime where k(F)a > 0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid.

Soliton dynamics at an interface between a uniform medium and a nonlinear optical lattice

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

Generalized neighbor-interaction models induced by nonlinear lattices

It is shown that the tight-binding approximation of the nonlinear Schrodinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dynamics obeys essentially the linear Schrodinger equation. We analyze the properties of such models both in connection to their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

Nonlinear Schrodinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

We introduce a nonlinear Schrodinger equation to describe the dynamics of a superfluid Bose gas in the crossover from the weak-coupling regime, where an(1/3)<<1 with a the interatomic s-wave scattering length and n the bosonic density, to the unitarity limit, where a ->+infinity. We call this equation the unitarity Schrodinger equation (USE). The zero-temperature bulk equation of state of this USE is parametrized by the Lee-Yang-Huang low-density expansion and Jastrow calculations at unitarity. With the help of the USE we study the profiles of quantized vortices and vortex-core radius in a uniform Bose gas. We also consider quantized vortices in a Bose gas under cylindrically symmetric harmonic confinement and study their profile and chemical potential using the USE and compare the results with those obtained from the Gross-Pitaevskii-type equations valid in the weak-coupling limit. Finally, the USE is applied to calculate the breathing modes of the confined Bose gas as a function of the scattering length.

Effective nonlinear Schrodinger equations for cigar-shaped and disc-shaped Fermi superfluids at unitarity

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

Matter-wave two-dimensional solitons in crossed linear and nonlinear optical lattices

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

Negative Even Grade mKdV Hierarchy and its Soliton Solutions

In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra (s) over capl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method based on non zero vacua. The sub-hierarchies admiting such class of solutions are classified.