Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Is the $\mathbb{Z}_2\times \mathbb{Z}_2$-graded sine-Gordon equation
  integrable?   We examine the question of the integrability of the recently defined
$\mathbb{Z}_2\times \mathbb{Z}_2$-graded sine-Gordon model, which is a natural
generalisation of the supersymmetric sine-Gordon equation. We do this via
appropriate auto-B\"{a}cklund transformations, construction of conserved
spinor-valued currents and a pair of infinite sets of conservation laws.

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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin