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