Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two new standing solitary waves in shallow water   In this paper, the closed-form analytic solutions of two new Faraday's
standing solitary waves due to the parametric resonance of liquid in a vessel
vibrating vertically with a constant frequency are given for the first time.
Using a model based on the symmetry of wave elevation and the linearized
Boussinesq equation, we gain the closed-form wave elevations of the two kinds
of non-monotonically decaying standing solitary waves with smooth crest and the
even or odd symmetry. All of them have never been reported, to the best of our
knowledge. Besides, they can well explain some experimental phenomena. All of
these are helpful to deepen and enrich our understandings about standing
solitary waves and Faraday's wave.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat