Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Justification of the NLS approximation for ion Euler-Poisson equation   The nonlinear Schr\"{o}dinger (NLS) equation can be derived as a formal
approximation equation describing the envelopes of slowly modulated spatially
and temporarily oscillating wave packet-like solutions to the ion Euler-Poisson
equation. In this paper, we rigorously justify such approximation by giving
error estimates in Sobolev norms between exact solutions of the ion
Euler-Poisson system and the formal approximation obtained via the NLS
equation. The justification consists of several difficulties such as the
resonances and loss of regularity, due to the quasilinearity of the problem.
These difficulties are overcome by introducing normal form transformation and
cutoff functions and carefully constructed energy functional of the equation.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin