Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The sine-Gordon equation on time scales   We formulate and discuss integrable analogue of the sine-Gordon equation on
arbitrary time scales. This unification contains the sine-Gordon equation,
discrete sine-Gordon equation and the Hirota equation (doubly discrete
sine-Gordon equation) as special cases. We present the Lax pair, check
compatibility conditions and construct the Darboux-B\"acklund transformation.
Finally, we obtain a soliton solution on arbitrary time scale. The solution is
expressed by the so called Cayley exponential function.

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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th