Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On complete integrability of the generalized Weierstrass system   In this paper we study certain aspects of the complete integrability of the
Generalized Weierstrass system in the context of the Sinh-Gordon type equation.
Using the conditional symmetry approach, we construct the B\"{a}cklund
transformation for the Generalized Weierstrass system which is determined by
coupled Riccati equations. Next a linear spectral problem is found which is
determined by nonsingular $2 \times 2$ matrices based on an $sl (2, \mathbb C)$
representation. We derive the explicit form of the Darboux transformation for
the Weierstrass system. New classes of multisoliton solutions of the
Generalized Weierstrass system are obtained through the use of the B\"{a}cklund
transformation and some physical applications of these results in the area of
classical string theory are presented.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph