2011
DOI: 10.1063/1.3623415
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Modulated amplitude waves with nonzero phases in Bose-Einstein condensates

Abstract: In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using the averaging method, we determine the location where the modulated amplitude waves (periodic or quasi-periodic) exist and obtain that all these modulated amplitude waves (periodic or quasi-periodic) form a foliation by varying the integration constant continuously. Compared with the previous work, modulated amplitude waves studied in this pape… Show more

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Cited by 15 publications
(9 citation statements)
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“…Since the reservoir permeability bound given by CNPC and Sinopec is 50 mD, whether ultra-lowpermeabilityreservoirs are suitable to use MOER draws attention. A pilot in an ultra-low-permeability reservoir was conducted in 2009 in Ansai in Changqing Oilfield [31,[66][67][68]. The average permeability of Ansai Oilfield is 1.29 mD, and the average porosity is 12.4%.…”
Section: Changqing Oilfieldmentioning
confidence: 99%
See 1 more Smart Citation
“…Since the reservoir permeability bound given by CNPC and Sinopec is 50 mD, whether ultra-lowpermeabilityreservoirs are suitable to use MOER draws attention. A pilot in an ultra-low-permeability reservoir was conducted in 2009 in Ansai in Changqing Oilfield [31,[66][67][68]. The average permeability of Ansai Oilfield is 1.29 mD, and the average porosity is 12.4%.…”
Section: Changqing Oilfieldmentioning
confidence: 99%
“…The well pattern is shown in Figure 15 [31,68]. Oil production before and after MRF is given in Table 7 [31,68] while reservoir parameters are given in Table 8 [31,[66][67][68]. Oil production indicates that microbial flooding can reduce water cut and increase oil production.…”
Section: Changqing Oilfieldmentioning
confidence: 99%
“…However, also in many cases, weak potentials or approximately constant potentials are typically used, such as ( ) = 0 + 1 ( ) with ≪ 1. Therefore, one can use the Lindstedts method and the multiple scale perturbation theory [13,14] or the method of averaging [15][16][17] to study dynamics of BEC with the high order approximation. For = 0, the solutions of system (1) with coherent structures may be equilibrium points, standing waves, solitary waves, or even unbounded.…”
Section: Introductionmentioning
confidence: 99%
“…For = 0, the solutions of system (1) with coherent structures may be equilibrium points, standing waves, solitary waves, or even unbounded. While the small perturbed parameter ̸ = 0, for example, Bose-Einstein condensed atoms being perturbed by a weak optical lattice potential, the dynamical characters of these solutions may be preserved [14,15] as periodic or quasiperiodic modulated amplitude waves. However, under some conditions of the adjustable parameters such characters may be destroyed, and the spatial chaos in the BEC occurs [6].…”
Section: Introductionmentioning
confidence: 99%
“…For instance, the existence of periodic orbits and the stability of system have been studied using averaging method in [22][23][24][25][26]. In the previous work [27], we have studied the existence of periodic orbits and their stability by using the classical averaging method for the three-particle timedependent FPU chains, where the system can be regarded as a perturbation of isochronous system.…”
Section: Introductionmentioning
confidence: 99%