Phase transition from soliton to breather, soliton-breather molecules, breather molecules of the Caudrey-Dodd-Gibbon equation

•The Caudrey-Dodd-Gibbon equation is under investigation.•The first- to fourth-order solutions are represented using the bilinear method.•The transition from soliton to breather, soliton-breather molecules and breather molecules are observed.