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1.
We present three families of one-soliton solutions for (2+1)-dimensional Gross-Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose-Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments. 相似文献
2.
W. P.?Zhong M.?Beli? R. H.?Xie G.?Chen Y. Q.?Lu 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,55(1):147-153
Bright and dark matter wave solitons are
constructed analytically in a three-dimensional (3D) highly anisotropic
Bose-Einstein condensate (BEC) with a time-dependent parabolic potential,
and numerical simulations are performed to confirm the existence and
dynamics of such analytical solutions. Different classes of bright and dark
solitons are discovered among the solutions of the generalized anisotropic
(3+1)D Gross-Pitaevskii equation. Our results demonstrate that the bright
and dark solitary waves can be manipulated and controlled by changing the
scattering length, which can be used to compress the second-order bright and
dark solitons of BECs into desired peak density. 相似文献
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4.
We investigate the exact bright and dark solitary wave solutions of an effective 1D Bose-Einstein condensate (BEC) by assuming that the interaction energy is much less than the kinetic energy in the transverse direction. In particular, following the earlier works in the literature Pérez-García et al. (2004) [50], Serkin et al. (2007) [51], Gurses (2007) [52] and Kundu (2009) [53], we point out that the effective 1D equation resulting from the Gross-Pitaevskii (GP) equation can be transformed into the standard soliton (bright/dark) possessing, completely integrable 1D nonlinear Schrödinger (NLS) equation by effecting a change of variables of the coordinates and the wave function. We consider both confining and expulsive harmonic trap potentials separately and treat the atomic scattering length, gain/loss term and trap frequency as the experimental control parameters by modulating them as a function of time. In the case when the trap frequency is kept constant, we show the existence of different kinds of soliton solutions, such as the periodic oscillating solitons, collapse and revival of condensate, snake-like solitons, stable solitons, soliton growth and decay and formation of two-soliton bound state, as the atomic scattering length and gain/loss term are varied. However, when the trap frequency is also modulated, we show the phenomena of collapse and revival of two-soliton like bound state formation of the condensate for double modulated periodic potential and bright and dark solitons for step-wise modulated potentials. 相似文献
5.
Dynamics of Bright/Dark Solitons in Bose--Einstein Condensates with Time-Dependent Scattering Length and External Potential 下载免费PDF全文
We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton's parameters (amplitude, width, and period) can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments. 相似文献
6.
Zhi-Yuan Sun Yi-Tian Gao Xin Yu Ying Liu 《International Journal of Theoretical Physics》2011,50(9):2776-2789
We investigate compression of the bright bound solitons in the Bose-Einstein condensates (BECs) by exponentially increasing the absolute value of the atomic scattering length. Similarity transformation and Hirota bilinear method are used to symbolically solve the one-dimensional nonlinear Schrödinger equation with the time-dependent coefficients. We present types of the bright bound solitons in compression through manipulating their initial coherence. Results show that the improved quantity of the atomic density peaks can be observed before the collapse of the solitons when their coherence is increased. Furthermore, we discuss how those compressed bound solitons are influenced by the adjacent solitons. The bound structures in our study are illustrated to exist with the parameters within the current experimental capacity (the spatial and temporal ranges of the bound solitons are less than 56 μm and 50 ms in our investigation), which suggests a future observation in the BECs experiments. 相似文献
7.
Dynamics of solitons in Bose-Einstein condensate with time-dependent atomic scattering length 下载免费PDF全文
The evolution of solitons in Bose--Einstein condensates (BECs)
with time-dependent
atomic scattering length in an expulsive parabolic potential is studied. Based on
the extended hyperbolic function method, we successfully obtain the bright and dark
soliton solutions. In addition, some new soliton solutions in this model are found.
The results in this paper include some in the literature ({\em Phys. Rev. Lett.}
{\bf 94} (2005) 050402 and {\em Chin. Phys. Lett.} {\bf 22} (2005) 1855). 相似文献
8.
9.
We analyze the dynamics of a bright soliton in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential. Under a safe range of parameters in which the Gross-Pitaevskii (GP) equation is effective in one dimension, our results show that, the dynamics of the bright soliton can be classed into two phases, depending on the value of the scattering length. Meanwhile, there exists a critical value of the absolute value of the atomicscattering length, below which, the dynamics of the bright soliton is very regular. Those phenomena can be useful for developing concrete applications of the nonlinear matter waves. We also obtain the orbital equation of the bright soliton and get some interesting data which may be useful for the experimental observation of the bright soliton and the application of the atom laser with manipulated intensity. 相似文献
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We obtain the bright matter wave solitons in Bose–Einstein condensates from a trivial input solution by solving the time dependent Gross–Pitaevskii (GP) equation with quadratic potential and exponentially varying scattering length. We observe that the matter wave density of bright soliton increases with time by virtue of the exponentially increasing scattering length. We also understand that the matter wave densities of bright soliton trains remain finite despite the exchange of atoms during interaction and they travel along different trajectories (diverge) after interaction. We also observe that their amplitudes continue to fluctuate with time. For exponentially decaying scattering lengths, instability sets in the condensates. However, the scattering length can be suitably manipulated without causing the explosion or the collapse of the condensates. 相似文献
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14.
《中国物理快报》2016,(10)
We investigate the moving matter-wave solitons in spin-orbit coupled Bose-Einstein condensates(BECs) by a perturbation method.Starting with the one-dimensional Gross-Pitaevskii equations,we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spinorbit coupling.The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs.We find different types of moving solitons:dark-bright,bright-bright and dark-dark solitons.Interestingly,moving dark-dark soliton for attractive intra- and inter-species interactions is found,which depends on the Raman coupling.The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin-orbit coupling. 相似文献
15.
The characteristics of solitons with a localized impurity in Bose-Einstein condensates (BECs) are investigated with numerical simulations of the Gross-Pitaevskii (GP) equation, the effects of the impurity on BEC solitons are discussed, and the atom population transferring ratios between the two BECs as time goes on are analyzed. It is found that population transfer depends on the impurity strength and the parameters of the system of BECs. 相似文献
16.
D. Zhao X.-G. He H.-G. Luo 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,53(2):213-216
In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schrödinger (NLS) equation. An integrable condition is first obtained by the Painlevé analysis, which is shown to be consistent with that obtained by the Lax pair method. Under this condition, we present a general transformation, which can directly convert all allowed exact solutions of the standard NLS equation into the corresponding exact solutions of the nonautonomous NLS equation. The method is quite powerful since the standard NLS equation has been well studied in the past decades and its exact solutions are vast in the literature. The result provides an effective way to control the soliton dynamics. Finally, the fundamental bright and dark solitons are taken as examples to demonstrate its explicit applications. 相似文献
17.
Feshbach resonance management of vector solitons in two-component Bose—Einstein condensates 下载免费PDF全文
We consider two coupled Gross-Pitaevskii equations describing a two-component Bose-Einstein condensate with time-dependent atomic interactions loaded in an external harmonic potential,and investigate the dynamics of vector solitons.By using a direct method,we construct a novel family of vector soliton solutions,which are the linear combination between dark and bright solitons in each component.Our results show that due to the superposition between dark and bright solitons,such vector solitons possess many novel and interesting properties.The dynamics of vector solitons can be controlled by the Feshbach resonance technique,and the vector solitons can keep the dynamic stability against the variation of the scattering length. 相似文献
18.
In the paper, a generalized sub-equation method is presented to construct some exact analytical solutions of nonlinear partial differential equations. Making use of the method, we present rich exact analytical solutions of the onedimensional nonlinear Schr(o)dinger equation which describes the dynamics of solitons in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential. The solutions obtained include not only non-traveling wave and coefficient function's soliton solutions, but also Jacobi elliptic function solutions and Weierstrass elliptic function solutions. Some plots are given to demonstrate the properties of some exact solutions under the Feshbachmanaged nonlinear coefficient and the hyperbolic secant function coefficient. 相似文献
19.
Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential 下载免费PDF全文
We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schrdinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly distributed.Such solutions exist in certain constraint conditions on the coefficients depicting dispersion,nonlinearity,and gain(loss).Various shapes of bright solitons and interesting interactions between two solitons are observed.Physical applications of interest to the field and stability of the solitons are discussed. 相似文献
20.
LI Hua-Mei 《理论物理通讯》2007,47(1):63-68
Evolution of periodic waves and solitary waves in Bose-Einstein condensates (BECs) with time-dependent atomic scattering length in an expulsive parabolic potential is studied. Based on the mapping deformation method, we successfully obtain periodic wave solutions and solitary wave solutions, including the bright and dark soliton solutions.The results in this paper include some in the literatures [Phys. Rev. Lett. 94 (2005) 050402 and Chin. Phys. Left. 22 (2005) 1855]. 相似文献