Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On stationary solutions of KdV and mKdV equations   Stationary solutions on a bounded interval for an initial-boundary value
problem to Korteweg--de~Vries and modified Korteweg--de~Vries equation (for the
last one both in focusing and defocusing cases) are constructed. The method of
the study is based on the theory of conservative systems with one degree of
freedom. The obtained solutions turn out to be periodic. Exact relations
between the length of the interval and coefficients of the equations which are
necessary and sufficient for existence of nontrivial solutions are established.

6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas