Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact solutions for chemical concentration waves of self-propelling
  camphor particles racing on a ring: A novel potential dynamics perspective   A potential dynamics approach is developed to determine the periodic standing
and traveling wave patterns associated with self-propelling camphor objects
floating on ring-shaped water channels. Exact solutions of the wave patterns
are derived. The bifurcation diagram describing the transition between the
immobile and self-propelling modes of camphor objects is derived
semi-analytically. The bifurcation is of a pitchfork type which is consistent
with earlier theoretical work in which natural boundary conditions have been
considered.

5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph