Soliton fission and fusion: Burgers equation and Sharma–Tasso–Olver equation

Fission and fusion phenomena can happen for solitons (sometimes solitary waves may be more accurate) which have been recently discovered both theoretically and experimentally. In this paper, taking the Burgers equation and the Sharma–Tasso–Olver equation as two concrete examples to show the fission and fusion of the solitary wave and the soliton solutions respectively which are studied by means of the Hirota’s direct method and the Bäcklund transformation. Furthermore, the amplitude and velocity relations between solitons and/or solitary waves before and after interactions are given and a possible general condition for fission and/or fusion is proposed.