Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Static solitons, Lorentz invariance, and a new perspective on the
  integrability of the Sine Gordon equation in (1+2) dimensions   Contrary to the common understanding, the Sine-Gordon equation in (1+2)
dimensions does have N-soliton solutions for any N. The Hirota algorithm allows
for the construction of static N-soliton solutions (i.e., solutions that do not
depend on time) of that equation for any N. Lorentz transforming the static
solutions yields N-soliton solutions in any moving frame. They are scalar
functions under Lorentz transformations. In an N-soliton solution in a moving
frame, (N-2) of the (1+2)-dimensional momentum vectors of the solitons are
linear combinations of the two remaining vectors.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex