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Two routes to the one-dimensional discrete nonpolynomial Schrödinger equation
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10.1063/1.3248269
/content/aip/journal/chaos/19/4/10.1063/1.3248269
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/4/10.1063/1.3248269
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Values of the transverse width as functions of the chemical potential for fundamental on-site solitons in model 1 (the ordinary model) are shown by curves, which are marked by triangles for the central site [in panel (a), the full and empty circles almost coincide]. full circles for the first neighbors, and empty circles for the second neighbors to the central site. In model 2 (the new system) the values of for fundamental on-site solitons are shown by dashed lines for the central site, dotted lines for the first neighbors, and dashed-dotted lines for the second neighbors to the central site. The intersite coupling constants are (a) and (b) .

Image of FIG. 2.
FIG. 2.

The same as in Fig. 1 but for families of intersite solitons found in both models 1 and 2.

Image of FIG. 3.
FIG. 3.

The cw solutions are unstable to modulational perturbations in regions below curves , which are determined by condition , see Eq. (29). The solid and dashed curves correspond to models 1 and 2, respectively. The figure pertains to and .

Image of FIG. 4.
FIG. 4.

The norm (power) vs chemical potential for on-site fundamental solitons in both models 1 and 2. The coupling constants are (a) and (b) , which correspond to strongly discrete systems and quasicontinual systems, respectively.

Image of FIG. 5.
FIG. 5.

The norm (power) vs chemical potential for intersite fundamental solitons in models 1 and 2. The coupling constants are (a) and (b) .

Image of FIG. 6.
FIG. 6.

Free energy vs norm for on-site and intersite fundamental solitons in both models 1 and 2 for (a) and (b) . Solid and dashed lines correspond to the on-site solitons in models 2 and 1, respectively. Dotted and dashed-dotted lines represent, respectively, intersite solitons in models 2 and 1.

Image of FIG. 7.
FIG. 7.

Pure real unstable eigenvalues (“ev”) for intersite unstaggered solitons in models 1 and 2 are shown by black and white circles, respectively, for . Note that in this case, pure real eigenvalues for on-site solitons have not been found.

Image of FIG. 8.
FIG. 8.

The same as in Fig. 7 but at . In this case, plots (a) and (b) display the eigenvalues for the on-site solitons and intersite solitons, respectively.

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/content/aip/journal/chaos/19/4/10.1063/1.3248269
2009-10-15
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Two routes to the one-dimensional discrete nonpolynomial Schrödinger equation
http://aip.metastore.ingenta.com/content/aip/journal/chaos/19/4/10.1063/1.3248269
10.1063/1.3248269
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