Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Genus-Two Solutions for the ILW equation   The existence of theta function solutions of genus two for the ILW equation
is established. A numerical example is also presented. The method basically
goes along with the Krichever's construction of theta function solutions for
soliton equations, such as the KP equation. This idea leads us to a question
whether a Riemann surface exists which allows a peculiar Abelian integral of
the third kind. The answer is affirmative at least for genus-two curves.

22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org