Fission and fusion of solitons for the (1+1)-dimensional Kupershmidt equation

By means of the heat conduction equation and the standard truncated Painlev e expansion, the (1+1)dimensional Kupershmidt equation is solved. Some sign ificant exact multi-soliton solutions are given. Especially, for the intera ction of the multi-solitons of the Kupershmidt equation, we find that a sin gle (resonant) kink or bell soliton may be fissioned to several kink or bel l solitons. Inversely, several kink or bell solitons may also be fused to o ne kink or bell soliton.