Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular solitons   We demonstrate that the commonly known concept, which treats solitons as
nonsingular solutions produced by the interplay of nonlinear self-attraction
and linear dispersion, may be extended to include modes with a relatively weak
singularity at the central point, which keeps their integral norm convergent.
Such states are generated by self-repulsion, which should be strong enough,
namely, represented by septimal, quintic, and usual cubic terms in the
framework of the one-, two-, and three-dimensional (1D, 2D, and 3D) nonlinear
Schroedinger equations (NLSEs), respectively. Although such solutions seem
counterintuitive, we demonstrate that they admit a straightforward
interpretation as a result of screening of an additionally introduced
attractive delta-functional potential by the defocusing nonlinearity. The
strength ("bare charge") of the attractive potential is infinite in 1D, finite
in 2D, and vanishingly small in 3D. Analytical asymptotics of the singular
solitons at small and large distances are found, entire shapes of the solitons
being produced in a numerical form. Complete stability of the singular modes is
accurately predicted by the anti-Vakhitov-Kolokolov criterion (under the
assumption that it applies to the model), as verified by means of numerical
methods. In 2D, the NLSE with a quintic self-focusing term admits singular
soliton solutions with intrinsic vorticity too, but they are fully unstable. We
also mention that dissipative singular solitons can be produced by the model
with a complex coefficient in front of the nonlinear term.

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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio