Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: WKB analysis for nonlinear Schr\"{o}dinger equations with potential   We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger
equation with a subquadratic potential. This concerns subcritical, critical,
and supercritical cases as far as the geometrical optics method is concerned.
In the supercritical case, this extends a previous result by E. Grenier; we
also have to restrict to nonlinearities which are defocusing and cubic at the
origin, but besides subquadratic potentials, we consider initial phases which
may be unbounded. For this, we construct solutions for some compressible Euler
equations with unbounded source term and unbounded initial velocity.

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The categories of this paper are: nucl-th
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: cs
10
The categories of this paper are: q-bio