Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the extension of the frequency maps of the KdV and the KdV2 equations   In form of a case study for the KdV and the KdV2 equations, we present a
novel approach of representing the frequencies of integrable PDEs which allows
to extend them analytically to spaces of low regularity and to study their
asymptotics. Applications include convexity properties of the Hamiltonians and
wellposedness results in spaces of low regularity. In particular, it is proved
that on $H^{s}$ the KdV2 equation is $C^{0}$-wellposed if $s\ge 0$ and illposed
(in a strong sense) if $s < 0$.

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th