Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential

Integrable nonautonomous nonlinear Schrödinger equations are equivalent to the standard autonomous equation

A class of nonautonomous nonlinear Schrödinger equations, claiming to be novel integrable systems with rich properties, continues to appear in the literature. All such equations are shown to be not new, but equivalent to the standard autonomous equation, which trivially explains their integrability features.

Discrete chaotic states of a Bose-Einstein condensate

We examine spatial chaos in a one-dimensional attractive Bose-Einstein condensate interacting with a Gaussian-like laser barrier and perturbed by a weak optical lattice. For a low laser barrier, chaotic regions of the parameters are demonstrated and the chaotic and regular states are illustrated numerically. In the high-barrier case, bounded perturbed solutions that describe a set of discrete chaotic states are constructed for discrete barrier heights and magic numbers of condensed atoms. Chaotic density profiles are exhibited numerically for the lowest quantum number, and analytically bounded but numerically unbounded Gaussian-like configurations are confirmed. It is shown that the chaotic wave packets can be controlled experimentally by adjusting the laser barrier potential.

Localized gap-soliton trains of Bose-Einstein condensates in an optical lattice

We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the nth energy band is a linear superposition of Mathieu's functions ce_{n-1} and se_{n} ; and the Bloch wave in the nth band gap is a linear superposition of ce_{n} and se_{n} . For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons-fundamental solitons (which is a localized and stable state) and subfundamental solitons (which is a localized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [B. Eiermann, Phys. Rev. Lett. 92, 230401 (2004)]. Furthermore, we predict that a localized gap-soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.

Exact solitonic solutions of the Gross-Pitaevskii equation with a linear potential

We derive classes of exact solitonic solutions of the time-dependent Gross-Pitaevskii equation with repulsive and attractive interatomic interactions. The solutions correspond to a string of bright solitons with phase difference between adjacent solitons equal to pi. While the relative phase, width, and distance between adjacent solitons turn out to be a constant of the motion, the center of mass of the string moves with a constant acceleration arising from the inhomogeneity of the background.

Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation

We present a large family of exact solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain or loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map onto a linear Schrödinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Streckeret al. [Nature (London) 417, 150 (2002)], spatiotemporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates, and analytical expression of two-soliton bound states, to name a few.