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arXiv · 1404.3539

The sine-Gordon equation on time scales

Jan L. Cieśliński·Tomasz Nikiciuk·Kamil Waśkiewicz
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Abstract

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-Bäcklund 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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Jan L. Cieśliński, Tomasz Nikiciuk, Kamil Waśkiewicz. 2014-04-14. The sine-Gordon equation on time scales. https://arxiv.org/abs/1404.3539

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