The sine-Gordon equation on time scales
Exactly Solvable and Integrable Systems
2014-04-15 v1
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-B\"acklund transformation. Finally, we obtain a soliton solution on arbitrary time scale. The solution is expressed by the so called Cayley exponential function.
Cite
@article{arxiv.1404.3539,
title = {The sine-Gordon equation on time scales},
author = {Jan L. Cieśliński and Tomasz Nikiciuk and Kamil Waśkiewicz},
journal= {arXiv preprint arXiv:1404.3539},
year = {2014}
}
Comments
16 pages