Exact solutions and conservation laws for a nonisospectral sine-Gordon equation

A bilinear form of a nonisospectral sine-Gordon equation is given. Exact solutions are further obtained through the Hirota method and Wronskian technique, respectively. Some nonisospectral characteristics of the obtained solutions, such as the time-dependent shape, time-dependent speed and some non-propagating solitary waves, are discussed. The conservation laws are derived.