Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Water-waves modes trapped in a canal by a body with the rough surface   The problem about a body in a three dimensional infinite channel is
considered in the framework of the theory of linear water-waves. The body has a
rough surface characterized by a small parameter $\epsilon>0$ while the
distance of the body to the water surface is also of order $\epsilon$. Under a
certain symmetry assumption, the accumulation effect for trapped mode
frequencies is established, namely, it is proved that, for any given $d>0$ and
integer $N>0$, there exists $\epsilon(d,N)>0$ such that the problem has at
least $N$ eigenvalues in the interval $(0,d)$ of the continuous spectrum in the
case $\epsilon\in(0,\epsilon(d,N)) $. The corresponding eigenfunctions decay
exponentially at infinity, have finite energy, and imply trapped modes.

10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga