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We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor “bubbles”, and topological excitations, in the form of dark solitons in 1D and vortices with winding number m in 2D. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with m=1, are completely stable, while the dark solitons and vortices with m=2 have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point.
Keywords
Nonlinear Schrodinger equation , Inhomogeneous nonlinear media , Flat-floor and flat-waist soltions , Precession of vortex solitons
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CURRENT STATUS: Under Review
Version 1
Posted 19 May, 2021
No community comments so far
Editorial decision: Minor revisions
On 18 Jun, 2021
Reviews received
Received 17 May, 2021
Reviewers invited
Invitations sent on 17 May, 2021
Editor assigned
On 12 May, 2021
First submitted
On 11 May, 2021
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Subject Areas
Mechanical Engineering
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This preprint is under consideration at Nonlinear Dynamics. A preprint is a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research Article
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Under Review
Version 1
Posted 19 May, 2021
No community comments so far
Editorial decision: Minor revisions
On 18 Jun, 2021
Reviews received
Received 17 May, 2021
Reviewers invited
Invitations sent on 17 May, 2021
Editor assigned
On 12 May, 2021
First submitted
On 11 May, 2021
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Mechanical Engineering
License:
This work is licensed under a CC BY 4.0 License. Read Full License
We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor “bubbles”, and topological excitations, in the form of dark solitons in 1D and vortices with winding number m in 2D. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with m=1, are completely stable, while the dark solitons and vortices with m=2 have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
The full text of this article is available to read as a PDF.
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