Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On multi soliton solutions of the Sine-Gordon equation in more than one
  space dimension   The (1+1)-dimensional Sine-Gordon equation passes integrability tests
commonly applied to nonlinear evolution equations. Its soliton solutions are
obtained by a Hirota algorithm. In higher space-dimensions, the equation does
not pass these tests. In this paper, using no more than the relativistic
kinematics of the tachyonic momentum vectors, from which the soliton solutions
are constructed through the Hirota algorithm, the existence and classification
of N-soliton solutions of the (1+2)- and (1+3)-dimensional equations for all N
greater than or equal to 1 are presented. In (1+2) dimensions, each
multisoliton solution propagates rigidly at one velocity. The solutions are
divided into two subsets: Solutions whose velocities are lower than the speed
of light (c = 1), or are greater than or equal to c.
  In (1+3)-dimensions, multisoliton solutions are characterized by spatial
structure and velocity composition. The spatial structure is either planar
(rotated (1+2)-dimensional solutions), or genuinely three-dimensional - branes.
Some solutions, planar or branes, propagate rigidly at one velocity, which is
lower than, equal to, or higher than c. A subset of the branes contains
hybrids, in which different clusters of solitons propagate at different
velocities. Some velocities may be lower than c but some must be equal to, or
greater than c. Finally, the speed of light cannot be approached from within
the subset of slower-than-light solutions in both (1+2) and (1+3) dimensions.

20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga