2014/04/14 by Cieśliński, Jan L., Nikiciuk, Tomasz, Waśkiewicz, Kamil
#34N05 #35Q51 #39A12 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences
paper · doi:10.48550/arxiv.1404.3539
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.