Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: N-soliton solutions to the DKP equation and Weyl group actions   We study soliton solutions to the DKP equation which is defined by the Hirota
bilinear form, \[ {\begin{array}{llll} (-4D_xD_t+D_x^4+3D_y^2)
\tau_n\cdot\tau_n=24\tau_{n-1}\tau_{n+1}, (2D_t+D_x^3\mp 3D_xD_y) \tau_{n\pm
1}\cdot\tau_n=0 \end{array} \quad n=1,2,.... \] where $\tau_0=1$. The
$\tau$-functions $\tau_n$ are given by the pfaffians of certain skew-symmetric
matrix. We identify one-soliton solution as an element of the Weyl group of
D-type, and discuss a general structure of the interaction patterns among the
solitons. Soliton solutions are characterized by $4N\times 4N$ skew-symmetric
constant matrix which we call the $B$-matrices. We then find that one can have
$M$-soliton solutions with $M$ being any number from $N$ to $2N-1$ for some of
the $4N\times 4N$ $B$-matrices having only $2N$ nonzero entries in the upper
triangular part (the number of solitons obtained from those $B$-matrices was
previously expected to be just $N$).

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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph