Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariance of white noise for KdV on the line   We consider the Korteweg--de Vries equation with white noise initial data,
posed on the whole real line, and prove the almost sure existence of solutions.
Moreover, we show that the solutions obey the group property and follow a white
noise law at all times, past or future.
  As an offshoot of our methods, we also obtain a new proof of the existence of
solutions and the invariance of white noise measure in the torus setting.

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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
18
The categories of this paper are: econ
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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin