Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collective Coordinate Methods and Their Applicability to $\varphi^4$
  Models   Collective coordinate methods are frequently applied to study dynamical
properties of solitons. These methods simplify the field equations - typically
partial differential equations - to ordinary differential equations for
selected excitations. More importantly though, collective coordinates provide a
practical means to focus on particular modes of otherwise complicated dynamical
processes. We review the application of collective coordinate methods in the
analysis of the kink-antikink interaction within the $\varphi^4$ soliton model
and illuminate discrepancies between these methods and the exact results from
the field equations.

27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph