Solitons in antiferroelectric liquid crystal and Josephson junction: The double sine-Gordon model

In this paper we solve the double sine-Gordon (sG) equation with constant coefficients using the Hirota bilinearization method and generalize the result with the director dynamics of antiferroelectric liquid crystal and fluxon excitation in the Josephson junction. The obtained one and two soliton solutions are consistently described for the above two systems with real physical parameters.