Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Breaking mechanism from a vacuum point in the defocusing nonlinear
  Schroedinger equation   We study the wave breaking mechanism for the weakly dispersive defocusing
nonlinear Schroedinger (NLS) equation with a constant phase dark initial datum
that contains a vacuum point at the origin. We prove by means of the exact
solution to the initial value problem that, in the dispersionless limit, the
vacuum point is preserved by the dynamics until breaking occurs at a finite
critical time. In particular, both Riemann invariants experience a simultaneous
breaking at the origin. Although the initial vacuum point is no longer
preserved in the presence of a finite dispersion, the critical behaviour
manifests itself through an abrupt transition occurring around the breaking
time.

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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg