Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cauchy problem for a fifth order KdV equation in weighted Sobolev
  spaces   In this work we study the initial value problem (IVP) for the fifth order KdV
equations, \begin{align*}
\partial_{t}u+\partial_{x}^{5}u+u^k\partial_{x}u=0,\text{} & \quad x,t\in
\mathbb R, \quad k=1,2, \end{align*} in weighted Sobolev spaces $H^s(\mathbb
R)\cap L^2(\langle x \rangle^{2r}dx)$. We prove local and global results. In
the case $k=2$ we point out the relation between decay and regularity of the
solution of the IVP.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con