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Explicit solutions to an effective Gross–Pitaevskii equation: One-dimensional Bose–Einstein condensate in specific traps
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10.1063/1.2834917
/content/aip/journal/jmp/49/2/10.1063/1.2834917
http://aip.metastore.ingenta.com/content/aip/journal/jmp/49/2/10.1063/1.2834917
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Density , given by Eq. (9), which is the linear function of potential . Here, the dotted line is the density itself, and the solid lines depict the potential for different values of constant . Other parameters are , , , and . Panel (a) corresponds to and . The solid black line corresponds to , while the solid red line corresponds to . Panel (b) corresponds to the limit of in Eq. (10). Here, , the solid black line corresponds to , and the solid red line to .

Image of FIG. 2.
FIG. 2.

Rescaled number of atoms per a potential well as a function of either parameter (a) or parameter [(b)–(e)] for some new solutions with the zero phase: (a) is the plot of for the new solution given by Eq. (11) for parameters and (b) and (c) are the plots corresponding to the new solutions given by Eq. (13) for . Note that (b) and (d) give the dependence of on for , while (c) and (e) give the dependence of on for .

Image of FIG. 3.
FIG. 3.

Phase and density , given by Eq. (20), as the square root of a rational function of potential . The parameters are , , , , , , , and . Potential (solid line) and density (dotted line) are shown in panel (a), while panel (b) displays phase .

Image of FIG. 4.
FIG. 4.

Potential (20) for different values of . The green line corresponds to , red line to , yellow line to , and black dotted line to .

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/content/aip/journal/jmp/49/2/10.1063/1.2834917
2008-02-07
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Explicit solutions to an effective Gross–Pitaevskii equation: One-dimensional Bose–Einstein condensate in specific traps
http://aip.metastore.ingenta.com/content/aip/journal/jmp/49/2/10.1063/1.2834917
10.1063/1.2834917
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