Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Construction of the mKdV Cyclic Symmetric $N$-soliton Solution by
  the B\"{a}cklund Transformation   We study group theoretical structures of the mKdV equation. The Schwarzian
type mKdV equation has the global M\"{o}bius group symmetry. The Miura
transformation makes a connection between the mKdV equation and the KdV
equation. We find the special local M\"{o}bius transformation on the mKdV
one-soliton solution which can be regarded as the commutative KdV B\"{a}cklund
transformation can generate the mKdV cyclic symmetric $N$-soliton solution. In
this algebraic construction to obtain multi-soliton solutions, we could observe
the addition formula.

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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org