Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steady periodic water waves under nonlinear elastic membranes   This is a study of two-dimensional steady periodic travelling waves on the
surface of an infinitely deep irrotational ocean, when the top streamline is in
contact with a membrane which has a nonlinear response to stretching and
bending, and the pressure in the air above is constant. It is not supposed that
the waves have small amplitude. The problem of existence of such waves is
addressed using methods from the calculus of variations. The analysis involves
the Hilbert transform and a Riemann-Hilbert formulation.

36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org