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Vortex collapse for the L 2-critical nonlinear Schrödinger equation
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10.1063/1.3608054
/content/aip/journal/jmp/52/8/10.1063/1.3608054
http://aip.metastore.ingenta.com/content/aip/journal/jmp/52/8/10.1063/1.3608054

Figures

Image of FIG. 1.
FIG. 1.

The real component of some vortex solutions.

Image of FIG. 2.
FIG. 2.

The radial component of some vortex solutions.

Image of FIG. 3.
FIG. 3.

Plots of the functions U (m) and Z (m) solving (3.8) for m = 1, 2, 3. The number of non-zero crossings determines the indexes of H 1 and H 2.

Image of FIG. 4.
FIG. 4.

Behaviour of the computed vortices as r becomes large. We recover the exponential decay.

Image of FIG. 5.
FIG. 5.

Asymptotically, the artificial boundary condition on the vortex is well satisfied.

Image of FIG. 6.
FIG. 6.

The asymptotical index function constants for winding numbers m = 1, 2, 3.

Image of FIG. 7.
FIG. 7.

Check of the artificial boundary conditions on the functions.

Image of FIG. 8.
FIG. 8.

Check of the artificial boundary conditions on the functions.

Image of FIG. 9.
FIG. 9.

Convergence of the approximate inner product values to their limiting states.

Image of FIG. 10.
FIG. 10.

Convergence of the approximate inner product values to their limiting states.

Tables

Generic image for table
Table I.

Inner products associated with for different winding numbers.

Generic image for table
Table II.

Inner products associated with for different winding numbers.

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/content/aip/journal/jmp/52/8/10.1063/1.3608054
2011-08-04
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Vortex collapse for the L2-critical nonlinear Schrödinger equation
http://aip.metastore.ingenta.com/content/aip/journal/jmp/52/8/10.1063/1.3608054
10.1063/1.3608054
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