Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions   Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional
Helmholtz equation are constructed in the case when the refractive index is a
sum of a constant and a small amplitude function which is periodic in one
direction and of finite support in the other. These solutions are quasiperiodic
along the structure and exponentially decay in the orthogonal direction. A
simple formula for the dispersion relation of these waves is obtained.

20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc